The Thunder announced Tuesday that Hill underwent a minor procedure to address an injury to his right thumb. He will be re-evaluated in four weeks.
If Hill is able to return within the four-week timeline, he could be back on the court by March 2. That would give interested teams at least a few games to evaluate how sharp he looks as they decide if they want to get involved in the bidding.
There's no reason for the Thunder to retain Hill. General manager Sam Presti has gone all-in on rebuilding and has been stockpiling draft picks over the past two years.
Hill, 34, won't be in Oklahoma City by the time the franchise is a legitimate playoff contender again. He is under contract through next season, but his deal is only partially guaranteed for $1.275 million in 2021-22.
In 14 games this season, Hill is averaging 11.8 points and shooting 50.8 percent from the field. He's also making 38.6 percent of his three-point attempts after leading the NBA with a 46 percent clip last season.