Tinsley, 35, spent the past two seasons in Utah. He played in 103 games, including 33 starts.
"There has been mutual interest," Raymond Brothers, Tinsley's agent, told The Tribune. Said coach Tyrone Corbin: "He has some interest, we have some interest. ... He's a guy who knows our system."
Burke's injury could provide Scott Machado the chance to make an impact in Utah. Depending on what the Jazz do with their roster while Burke is out, Machado might not only make the team but he could inherit a significant role.
"I came in fighting for life," Machado said. "... It's so bad something like that had to happen [to Burke]. But when the opportunity shows, I have to take advantage of it."
Machado spent most of last season in the NBA Development League, but he also played briefly with Houston and spent time with Golden State.
"I feel like I know how to lead a team," he said. "I know how to help a team get a good shot. ... [I] just try to run a team as well as possible."
Said Corbin: "Scott is pushing the pace the way we want. He's getting more and more comfortable on the floor. It's a big opportunity for him. ... Now, will he step up and get it done? I think he will relish the opportunity."
On the mend
Jazz veterans Marvin Williams and Brandon Rush continue to recover from injuries, but neither is close to returning.
Williams underwent surgery June 4 to repair his right heel and Achilles tendon.
When he was with Golden State, Rush tore his ACL and MCL in a game on Nov. 2. He underwent surgery in January.
According to Corbin, Rush is scheduled to be re-evaluated on Oct. 26. Williams' next visit with doctors will be "a little sooner."
"They are both getting closer every day," Corbin said. "... They are both supposed to start increasing their activity on the floor. But to go 5-on-5 is a ways off for them."
Meanwhile, Gordon Hayward suffered a bruised arch in Saturday's 106-74 loss to the Los Angeles Clippers. He did not practice Monday but did practice Tuesday and is expected to play Wednesday against Portland.
"It hurt," he said. "But it should be all right fine."