Players including Foye, Tinsley and Carroll all said they hoped to re-sign with the Jazz in the offseason.
"I want to be here," Foye said. "I just feel as though, no matter what nobody else do, it's all about me. I feel as though this is the place for me."
As many as 10 players will be free to sign elsewhere in the summer when they officially become free agents on July 1. Jefferson and Millsap are the headliners, but the Jazz could opt to let them go and be replaced by young big men Derrick Favors and Enes Kanter.
So, what about the rest of the free agents?
Williams, a key to the Jazz's successes, but also their shortcomings when he missed 32 games due to right thumb surgery, said he would like to return to the Jazz, but that it's not necessarily up to him.
"I think it's the ball is in their court," Williams said. "And I think it's more so what direction they want to go. They know how I feel, I know how they feel, so we'll see what happens."
The 35-year-old Tinsley said he thinks he can play "three or four more years" in the NBA, despite being signed to the Jazz in 2010 out of the D-League.
"Hopefully I come back," he said. "If not, it was a good two years for me. I helped a whole lot of young guys develop."
Williams was drafted by the Jazz with the 47th pick in 2004, but signed with Milwaukee after his rookie season. Later, he left the Bucks for Cleveland. It's a routine the one-time All-Star is plenty familiar with.
"We as basketball players," Williams said, "we just sit by the phone in the summertime and the agent and [Jazz executives] Kevin [O'Connor] and Dennis [Lindsey], they do all the talking. We just say, 'Oh, OK. Oh, OK. Sure. Oh. OK. Really?' That's about all that will come from my mouth. That's why we pay our agents and that's why we put our trust in them and let them have our best interests."
The Jazz are likely to build around Favors, Kanter and Gordon Hayward, but are salary cap-rich after missing the playoffs for the second time in three years. The Jazz hold a team option on rookie Kevin Murphy, and Marvin Williams holds an early termination clause.
In the end, just five players on the roster have guaranteed contracts for next season, which likely means the busiest offseason in team history.
Lindsey, the general manager, said he thinks the Jazz can attract quality free agents, if not retain members of the current team.
"I think we have a great story to tell about the history of the organization," Lindsey said. "I think we have plenty of roster spots and a lot of salary cap to pay good players."
Jazz players' statuses
Al Jefferson • Free agent. Paul Millsap • Free agent. Mo Williams • Free agent. Randy Foye • Free agent. Jamaal Tinsley • Free agent. Earl Watson • Free agent. DeMarre Carroll • Free agent. Marvin Williams • Early termination clause. Kevin Murphy • Team option. Jerel McNeal • Non-guaranteed contract.
Saturday's NBA playoff games
O Boston at New York, 1 p.m., Ch. 4
• Golden State at Denver, 5:30 p.m., ESPN
• Chicago at Brooklyn, 6 p.m., ESPN
• Memphis at L.A. Clippers, 8:30 p.m., ESPN