According to Shams Charania of The Athletic, the two sides will meet in Los Angeles this week and could have a "quick agreement" if the Warriors offer a five-year, $190 million contract.
On the other hand, Thompson would reportedly be willing to speak to the Los Angeles Clippers about a deal if the Warriors don't offer him the max.
The 29-year-old suffered a torn ACL in the NBA Finals, which could cost him all of next season or at least several months. However, Golden State has insisted his or Kevin Durant's injury won't affect the team's plans in free agency.
"All I'll say is that those guys are highly important to us and deserving of being rewarded in the right manner," general manager Bob Myers said, per Nick Friedell of ESPN. "... It's hard to find high-quality people, and both of them are that. And so you just—try to keep those guys within these walls the best you can."
Meanwhile, Thompson and his camp haven't given any indication they want to look elsewhere in free agency.
His father, Mychal Thompson, said earlier this month there's "no question" the player will re-sign with the Warriors and expected the five-year max deal, per Connor Letourneau of the San Francisco Chronicle.
Although there could be more competition to re-sign Durant, it appears as though the ball is in the Warriors' court when it comes to Thompson.