Shane Williams, also part of 2005 and 2009 tours, is also nearing a return and is targetting Wales' first training camp in Poland next month as he continues his recovery from the knee injury he suffered against Ireland in March.
A third Lion, Leigh Halfpenny is also hoping to make the trip to Poland following his latest ankle injury.
Jenkins underwent the procedure in February, and missed the entire RBS 6 Nations, in a bid to rectify a long-standing calf problem. But along with Exeter-bound prop Craig Mitchell, the two-tour Lion is back in full training.
Scarlets hooker Ken Owens has also joined the preliminary World Cup squad, to cover for Richard Hibbard who faces a 10-12 week lay-off after shoulder surgery.
"Both Gethin and Craig are back in full training and Richard has been given a return to play time of 10 to 12 weeks, which makes it possible for him to be back to fitness by the end of August," said Prav Mathema, Welsh Rugby Union national medical performance manager.
"Shane will be three more weeks before he is fully integrated into the training programme, which means he should be up to speed by the time we go on that first camp in Poland," added Mathema.
"Leigh is doing well after a successful operation on his foot, he is six weeks down the line now and able to start lifting weights again and also hopes to be at Spala."
The majority of the squad have begun their personal training programs although the rest and rehab periods have been extended for certain players.
The squad will embark on two separate and bespoke training camps in Spala, Poland, from July 2 to July 11 and from July 18 to July 26, with players selected for these camps based on their individual training requirements.
Wales face England at Twickenham on Saturday August 6 in the first of three remaining warm-up matches.
A week later they host Martin Johnson's team at the Millennium Stadium on Saturday, August 13, before taking on Argentina, again at home, on Saturday, August 20.
Gatland will then name a final squad Rugby World Cup on Monday, August 22, with the squad due to fly out to New Zealand on August 31.