The 33-year-old was expected to be ruled out of action until October after developing a blood clot in the lung following a back operation in March.
However the former England stopper, who has not played for Blackburn since December, hopes that he will be fit in time for the new season.
"I'm still on the warfarin [medication] at the moment," he told Sky Sports News. "Luckily I went to see a chest expert yesterday and she X-rayed my chest again and my chest looks clear. I've been given the go-ahead to start physical training again, which is really positive for me because I can start my fitness training.
"But because of the warfarin, I can't put the gloves on again. First of all, they diagnosed until October but hopefully it will be moved forwards now because everything's moving.
"It's looking like I'm going to be fit for the start of the season. I can put the gloves on at the end of July now."
Robinson has made 172 appearances for Blackburn since joining the club in 2008.