Jenkins also fractured a cheekbone in the momentous second Test against the Springboks on the Lions' summer tour of South Africa but he has now claimed that he could be back in action as early as next month.
"I'm hoping to be back by October, but maybe November," Jenkins told BBC Wales' Scrum V TV show.
"I just want to get fit first - it was a long season last year.
"I think everyone was carrying injuries, I think everyone does hide them so they can get on the Lions tour.
"So personally I just want to get as fit as I can when I get back playing and it's a big season for Wales again."
Jenkins earned two Lions caps in 2009 to add to the three he collected four years ago when Sir Clive Woodward's squad toured New Zealand.
After an impressive display in the first half of the second-Test in Pretoria, Jenkins was expected to play a leading role in closing stages of the three-match series before injury forced him to withdraw from the battle with just under a game-and-a-half to play.
His loss, alongside that of fellow Welsh front row Adam Jones was lamented by Lions coaches and supporters alike as the Springboks clinched series victory while Jenkins headed off for surgery in South Africa.
Jones, who is currently recovering from shoulder surgery and has recently signed a new contract with the Ospreys, told Scrum V that he hopes to playing again in December.