Rose tore his left ACL in Game 1 of the Eastern Conference quarterfinals against the Philadelphia 76ers on April 28. He had surgery on May 12.
Rose has been rehabbing in Los Angeles for about two weeks, Reggie said.
"He's walking without a (brace)," Reggie said. "He's way ahead of schedule.
"It's just keeping him focused, and we're not trying to rush him. Basically, just rehab, rehab, rehab. We haven't put nothing basketball in his face."
Dr. Brian Cole, who performed the surgery on Rose, also said in June that Rose was ahead of schedule.
Reggie said Rose being in Los Angeles allows him to relax and not worry about all the attention he receives in his hometown of Chicago.
"It's just a peace of mind," Reggie said. "He can't do too much in Chicago. The other day I talked to him, he was at Target just picking up stuff. Stuff like that, you can't do in Chicago."
Rose has yet to speak publicly since his injury, but Reggie said he would in due time. It just wasn't their focus right now.
"Eventually, he will," Reggie said. "Just for now, he's getting his mind right and is out in in California."