The 29-year-old, widely regarded as one of the best tight-heads in the world, has been sidelined since the Ospreys Heineken Cup defeat at London Irish.
The Ospreys have refused to pencil in a comeback date for Jones, instead preferring to ease the devastating scrummager back into training.
"Adam is five weeks post-injury now," said Ospreys physio Chris Towers.
"The problem has settled down well. We are starting to increase his functionality during rehab this week, after which we will be in a position to target a game for his return to action."
Jones has a slim chance of making the final rounds of the Six Nations but in order to do so he would need to return for the Ospreys against Glasgow on March 5. But that looks unlikely as both the Ospreys and Wales look to safeguard the remainder of his season.
Jones made six appearances for the Lions during the tour of South Africa and famously tamed 'the Beast' Tendai Mtawarirain the second Test.
The Lions' scrum had been backpedalling at a rate of knots. But the introduction of Jones and Matthew Rees as replacements, to form an all Welsh an all-Welsh front-row, saw the Lions get on the front foot and launch a second-half comeback.
They ultimately came up short but the image of Jones rescuing the Lions scrum will live long in the memory of all Lions fans.