The 76-times capped loosehead prop has been sidelined since January after going under the surgeon's knife to rectify a toe injury which had been the cause of long-standing calf problems.
Jenkins missed the entire RBS 6 Nations campaign but has returned to training in the past weeks and is nearing a Blues comeback.
"Gethin has worked very hard on his fitness," said Blues director of rugby Dai Young.
"He's done a bit of skills, he's running and he's starting to do some contact. He's only three or four weeks off it now.
"He's certainly hoping to get a couple of games in towards the end of the season.
"People know me well enough to know the players come first. If he's not fit enough to play any of the games, he won't play in any of them.
"It's as simple as that. We are not going to push him back until he's ready, but he's certainly targeted games before the end of the season.
"There's no reason why he shouldn't feature in a couple of games."
Jenkins could return for the home clash with Benetton Treviso on April 21, but if not the crunch Welsh derby with the Scarlets on May 6.
Meanwhile fellow prop John Yapp is targetting an earlier return, having missed the clash with the Ospreys with a calf strain.
Yapp is hoping to be available for the trip to Galway to face Connacht on April 15.
The return of two international props will be a much-needed tonic for the play-off chasing Blues who struggled at the set-piece at the Liberty Stadium.
"John will be back for our next game and Gethin's not going to be far behind him, which is great," added Young.
"They'll to play a big part in patching up some of our deficiencies."
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