There aren't really contending teams with cap space. There are some hopeful clubs that could let their bigger free agents walk to make a chunk, but it's arguable if they'd still even hopeful contenders if they did that. He could take less to sign with those teams. But it's not clear if winning a le is his primary goal at this point. Money might be the goal, or playing for Pop, or getting to see Wemby up close or extending his career. We don't know if other teams would see the same benefit from signing him. Like LAL has Davis who's at the point in his career where he really should be playing the bulk of center minutes. Cleveland needs to clear up center minutes more than add to that log jam. Dallas could really use him and may sign him, but only if Kyrie walks, in which case I don't know that they're more compelling. They're also limited in how much they can offer, seeing as they would need to find a new starting guard.
If Lopez doesn't reup with MKE (which is probably the likeliest outcome by a fair margin) I think it'll come down to issues the Spurs can definitely compete on. I know I might be coming off as a big Lopez stan, but in reality I am standing on the table this much because I want STers to open their minds beyond fantasizing that this specific collection of players is going to be the new Big Three that drives the team to success for the next two decades. It's mythologizing that era of the team by looking at their legacy as an inevitable result of the starting pieces rather than the dynamic and honestly sometimes slap-dash series of transactions or improvements the team made and failed to make over the course of more than a decade. In an extremely short span of time (from 2000-2004), the Spurs ran legit risks of losing each of the three at least once, and as second and third contracts came up for negotiation, it wasn't always clear the core was going to stay together. It's only after everyone got old and won multiple les did the inertia really kick in and it became more likely than not that the players would take whatever discounts to make it work as a trio. Even then you had Tony's trade speculation in 2011 and Manu's flirting with Philly in 2016.
That's a long-winded way of saying the Spurs need to make moves to help accomplish their goals in 2023, with only a vague sense of what they mean for 2027. Those future moves will be made then, not now.