The former England stopper was thought to be out until October after developing a pulmonary embolism (blood clot in the lung) following a back operation in March.
However the 33-year-old - who has not played for Blackburn since December, having fallen out of favour while Henning Berg was in charge - hopes to be back by the start of the 2013/14 campaign.
He told Sky Sports News: "I'm still on the warfarin (medication) at the moment.
"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."
He added: "Hopefully by July I can start training again and from then on, it (warfarin) only takes 48 hours to get out of the system and you're good to go I think."
Regarding his future at Blackburn, he said: "My contract was extended at the beginning of last season. There was an option to do that and at the moment, I've got two years left at Blackburn.
"I'm not sure where that's going to lead me because there have been other options. I'll just have to wait and see when I get back fit again."
When asked if he would be happy to stay at managerless Rovers, Robinson replied: "At the moment, yes.
"I don't know what is going on. With previous managers, we've had different conversations. Until there's an actual manager in place to have a conversation with about my own personal future, I'm just concentrating on getting myself fit and getting myself back."