The loose-head prop has been sidelined for the past three months after undergoing toe surgery to solve a long-standing calf problem.
Jenkins subsequently missed the entire RBS 6 Nations but he is set to return to action for the Cardiff Blues against Newport Gwent Dragons on April 29.
It had been hoped that Jenkins would be available for this weekend's Magners League clash with Connacht.
The 30-year-old, who has toured New Zealand and South Africa with the Lions in 2005 and 2009, is back running but needs an extra week due to be fully-fit for scrum time.
"We were hoping for Gethin to be available for this game, but he's not quite where he wanted to be," said Blues director of rugby Dai Young, himself a three-tour Lion.
"He's running. It's just that pressure point from the scrum is the issue more than anything."
"You've got to set yourself realistic targets. If things don't progress as quickly as possible, players don't play. It's as simple as that. We are not going to risk players.
"Realistically the target has moved back a couple of weeks to the Dragons game now."
The news will also be a major boost to Warren Gatland who will be delighted to see Jenkins get some game time under his belt ahead of Wales' World Cup warm-up matches.
Wales face the Barbarians on June 4 before Autumn matches with England, home and away, and Argentina.