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With Andrew Wiggins already signed (for better or worse) to a maximum contract, the Timberwolves now aim themselves after their first playoff season since 2004 toward a summer in which they must decide if and how they can sign All-Stars Jimmy Butler and Karl-Anthony Towns to similar deals as well.

When or if they do, they also must determine how they can assemble a competitive roster around a team that would dedicate most of its rising payroll to three players.

Could they create some flexibility to improve their three-point shooting and defense by trading backup center Gorgui Dieng, who has three years and more than $48 million left on a contract that looked reasonable in October 2016 when money was flooding into the salary cap from a massive new TV deal and Dieng still was a productive starter. Now it’s a commitment few teams would be willing to make.

Might they try to trade Wiggins and his deal worth at least $146 million before it even begins this next season? Guaranteed such a big contract last fall, Wiggins delivered a season in which he said he “learned a lot” while learning how to play with Butler on the perimeter. He also said, “I don’t think I had the best season,” a statement some Wolves fans consider the euphemism of the year.

Timberwolves owner Glen Taylor calls decisions to sign both Butler and Towns “big issues” about which he wants to give himself, coach/president of basketball operations Tom Thibodeau and General Manager Scott Layden time to ponder after their just completed 47-victory season and the next season ahead before they start making such big decisions.

“Well, we’re working on it,” Taylor said.

From there, the Wolves must decide whether to re-sign veteran guard Derrick Rose, a Thibodeau favorite who was effective in the playoffs. And can they afford to keep upcoming restricted free agent Nemanja Bjelica, who intrigued at least two NBA teams with money to spend this summer when he became a starter after Butler sustained a February knee injury and played well.

“I don’t know what I can say right now,” Bjelica said after Wednesday’s Game 5 loss. “I hope I will stay here. We will see. We had bad luck to play against Houston in the first round, but we have a great group of people here. First time in playoffs in 14 years is very important for us. I like it here.”

Veteran guard Jamal Crawford has a player option for next season and said he won’t begin to contemplate that decision until he decompresses from this past season. Backup point guard Tyus Jones, a member of Towns’ 2015 draft class, will be eligible to sign a contract extension this summer, and little-used veteran center Cole Aldrich can be paid off $2 million of the nearly $7 million owed him next season if he is waived by June 20.

All about Jimmy

It’s fitting that Butler is the first domino — a piece of his favorite game at which he calls himself unbeatable — from which the Wolves’ future will fall.

If they can’t convince him to stay and sign an extension, they would have to consider trading him before he can opt out of his contract in summer 2019 and leave.

Thibodeau traded lottery picks Zach LaVine, Kris Dunn and the draft rights to Lauri Markkanen to Chicago for Butler and the No. 16 pick in the draft last summer, which turned out to be Justin Patton.

In return, the Wolves received an experienced, tough, proven All-Star whom Thibodeau said meant “everything” for a team that won 16 more games than the season before and played in the postseason for the first time since the 2004 Western Conference final.

Butler potentially lost tens of millions dollars when the Bulls traded him away. Had he stayed he might have earned a chance at a “super max” contract. He still could earn tens of millions dollars more from the Wolves than he can get from another team if he signs an extension. They get a head start by being eligible to sign him this summer before he can opt out after next season.

Earlier this season, he said he’ll determine his future based upon wherever he feels he has the best chance to win big — “got to win” — and last week he told the Chicago Sun Times he’ll base it upon “being wanted and winning.” He said he already has earned enough money in his career and won’t let it dictate his decision. Without naming names, Butler this season criticized his younger teammates’ willingness to defend and their drive compared to his.

Taylor calls Butler a “very important part of our future” who brings a “personality and a skill-set” that’s different from his team’s younger players.

Butler turns 29 in September. Towns is a 22-year-old who is next in line after Wiggins to receive one of two maximum five-year contract extensions the Wolves can offer to players coming off their rookie deals.

Saying he still feels good about his investment in Wiggins, Taylor noted his team drafted Towns first overall, praised his yearly improvement and said about signing him for five more years, “That’s important. There’s no reason he isn’t involved in our long-term plans because he is such a young person.”

Finding value

If the Wolves do sign both Butler and Towns, they’ll need to surround them with personnel moves on a thrifty budget. Taylor said he’s hopeful his team “in a league of stars” can become the sort of destination franchise that Golden State, Houston and others are, able to attract veteran free agents willing to play for less so they can win big.

He also said it’d help if his team can strike big in the draft — like Utah did with 13th overall pick Donovan Mitchell — and find an impact player on a cost-efficient rookie contract. Last summer’s pick, Patton, played four NBA minutes in his rookie season and has had two foot surgeries since July.

The Wolves own the 20th pick in the June draft.

Among those players the Wolves already have, Rose is a player you’d expect Thibodeau will pursue hard to sign. Rose, because of multiple knee surgeries, isn’t the player he was when he won the 2011 league MVP award, but Thibodeau knows him, trusts him and Rose was one of the most consistent players in his role during a five-game series loss to Houston in the playoffs.

“The last two places I was at, they didn’t need my services,” Rose said before the season ended Wednesday. “So I come in here and they gave me the opportunity and the space to play the way I normally play. … Not to boast or brag, I know the type of player I am.”

Late Wednesday night, Thibodeau said his team must follow what he called a “major jump” by getting better next season.

“Just continue to build,” Thibodeau said. “We need another strong summer, another strong fall. We need everyone to commit to improve and learn and it never ends. That’s the thing about this league. You’re always going to be challenged.”

Twitter: @JerryZgoda E-mail: jzgoda@startribune.com

Blog: startribune.com/wolves