"We're not ruling him out for the whole conference finals, but we're not saying he's going to play, either," Kerr said. "It would be a long shot for him to play, but I think it's a possibility."
Payton fractured his left elbow in Game 2 of the Western Conference semifinals against the Memphis Grizzlies when Dillon Brooks hit Payton in the head while he was airborne during a fast-break dunk attempt.
Payton was initially estimated to miss approximately one month.
Brooks was ejected from the game after the foul was deemed a flagrant foul 2, and was later suspended from Game 3 for the play. Kerr said Brooks "broke the code" with the foul, which was not well-received by the Grizzlies, who said Brooks is not a dirty player.
Payton says he and Brooks have spoken since the incident and have cleared the air.
"It's all good," Payton said. "It's a basketball play. I know he didn't mean it. No hard feelings, no bad blood."
"NBA playoff foul, that's about it. It is what it is. It happened. Just didn't catch myself and things happened. But it's past me. It's behind me. I'm just trying to work and continue to strengthen my arm and get back, get ready to come back and help my team."
At first, Payton thought he had just hyperextended his elbow. It wasn't until he underwent an MRI that he learned it was a fracture.
Payton, who is left-handed, is no longer wearing a brace, but he has not been able to return to doing upper-body workouts. His work has mainly consisted of conditioning and lower-body strengthening work.
"He won't play to start out the series but the good thing with it being an elbow, he is able to do a lot of things on the court," Kerr said. "He is able to work his conditioning and his movement. If it was a knee or a foot and you can't do anything on the court, it takes a lot longer to recover."
Kerr continued: "All in all, Gary is doing well, we just don't know his availability. But, he is able to maintain his conditioning and do some things out on the court, which is important."
Payton said the thing he needs most to get back out on the court is time.
"I'm getting better every day, feeling better every day, but it's going to take time," Payton said. "We're not trying to set a date on when I can or when I can't [come back] or whatever. So just take it one day at a time."