According to ESPN's Bobby Marks in his Bulls' offseason guide (subscription required), the list of current teams besides San Antonio with an available $36.6 million max slot includes the Orlando Magic, Indiana Pacers, Detroit Pistons, and Portland Trail Blazers.
While Portland is more of a long shot given their financial situation, ESPN's Brian Windhorst recently suggested they're still at least an option.
"Eric Bledsoe's contract is on the books for $19 million," said Windhorst on The Hoop Collective Podcast. Only a fraction of that is guaranteed though. "So if they waive him, they can clear of $16 million there. "Hart's contract next season is not guaranteed, but the pickup date is June 25th. If they waive him, that is telegraphing that they think they'll be able to spend their free agent money."
As Bobby Marks notes, however, they'd also have to renounce Jusuf Nurkic to have enough to offer LaVine a max deal.
Judging by all the gymnastics it would take plus the outlook for Portland's immediate future, I think they can probably be ruled out as a serious contender for poaching LaVine.
Marks and Windhorst look at other possible options for LaVine
"I'm sure Orlando would be interested in a guy like LaVine, but I'm not sure Zach is ready to go there. Zach would not really match Oklahoma City's timeline. The Knicks wouldn't have the space. Is there another spot you can think of where it would make sense?" Windhorst asked Marks.
"The only other one would probably be Detroit, alongside Cade [Cunningham]," responded Marks. "That's a big number though. But it would be fascinating if he takes $56 million less to go somewhere else."
As Bobby mentioned earlier in the episode, the Bulls can offer $56 million more than any other team can this summer, which could be the deciding factor in him ultimately staying in Chicago. Neither Windhorst nor Marks mention San Antonio in this particular episode, but Marks does mention them as a team with the money to do so in his Bulls' offseason guide.
Ultimately, it's going to come down to how much LaVine believes he's worth and if the Bulls agree. While a five-year max contract would certainly be risky given his injury concerns, it's not out of the realm of possibility. Another team like the Spurs or Pistons making a serious offer for him is also in play considering his talents.
With the recent news that LaVine is expected to have a knee procedure with a complete recovery in the coming weeks, it's going to be very interesting to see which teams make real plays for the two-time All-Star.