It sure sounds like Austin Reaves wants to be a Los Angeles Laker next season ... but not only that -- he tells TMZ Sports he'd love to "run it back" with LeBron James, too!!

We caught up with the upcoming free agent after the Purple and Gold's playoff exit ... and asked how he'd feel about getting the King to stay in L.A.

Of course, Reaves would have to put pen to paper himself before he thinks ahead to the 2026-27 roster ... but Lakers Nation has gotta be wondering how they could've done this postseason if everyone was healthy.

The team dealt with notable injuries from Luka Dončić and Reaves himself ... and the Lakers were swept in the Western Conference Semifinals at the hands of the Oklahoma City Thunder.

27-year-old Reaves is expected to decline his player option and test the market ... and after his best season yet statistically (23.3 points, 5.5 assists and 4.7 rebounds a game), a bunch of teams are gonna try to sign him -- but it feels like he wants to stay.

As for LeBron, there are MUCH bigger question marks around his next move ... but Reaves would be on board with giving it another shot as a healthy Lakers squad.