The 2009 Lions Man of the Series hobbled out of Wales' Triple Crown victory over England at half-time with damaged medial ligaments.
But the star centre, who made five appearances for the Lions in South Africa, is making good progress as he battles to return to full fitness.
"We're waiting to find out more on Jamie, but it will probably be touch and go for the Italy game," said fellow former Lion Jenkins.
"He's progressing really well, rehabbing very well at this moment in time, so fingers crossed, he could well make that game."
Wales are also set to welcome back Matthew Rees and James Hook, also tourists to South Africa, for the Millennium Stadium clash with the Azzurri but Huw Bennett remains a major doubt.
Rees failed to recover in time from a calf injury to face the old enemy but is back in full training and is aiming to make his first Six Nations appearance of the year following an injury-ravaged six-months.
Hook remains with Perpignan in France but has overcome his bout of chicken pox and is set to feature in the Top 14 clash with Agen before returning to Wales.
"Smiler is also back training, so there's good news on that front," added Jenkins.
"He's back with us, so hopefully he'll be back and available for selection.
"Hooky is also going to be back to full fitness. I think he'll be involved for Perpignan this weekend and if he comes through that unscathed he'll be involved with us next week and the game after."
Wales remain unbeaten in the Championship and face Italy on March 10, in the penultimate match before a potential Grand Slam decider with France.
Jenkins insists Wales' only focus is on the clash with Italy and he expects a difficult encounter.
"We have a very tough game with Italy a week on Saturday and are not looking beyond that. If we can win it would set us up for a Grand Slam game with France, but we are looking at things one game at a time.
"Italy are always strong and will be strong up front this time. They are going to come and play, have a tough physical game and will want to take us on in the set-piece.
"They caused Ireland problems into the second-half last weekend and they should have beaten England at home. We know it's going to be a very tough afternoon for us, but we'll look forward to it.
"I'm expecting them to come here with four wins from their four games. England and Ireland will be tough for them, but France are at home and you'd expect them to win those games and hopefully come to Cardiff for a Grand Slam decider.
"But we have to just focus on ourselves and make sure we beat Italy."