Bishop is the Ospreys' joint record appearance holder but hasn't featured for Wales since June 2012 and wasn't available for this year's RBS 6 Nations due to the injury.
"I'm working really hard on my rehab and will hopefully be running again later this week. It's going really well," he said.
"Things are on target for me to take part in pre-season.
"I've never suffered much with injuries during my career, so it was disappointing to have to sit out four months of the season, but I've got to move on now and look forward.
"I have to crack on over the next few weeks to make sure I'm ready.
"I am going to work hard over the next two months as I want to win back my jersey."