Jenkins knew the potential ramifications when he signed for Toulon last summer and it is understood his loyalty in any tug-of-war would be with the club.
The Lions open their 10-match tour against the Barbarians in Hong Kong on June 1 - the same day as the Top 14 final - and coach Warren Gatland wants his whole squad to fly out together.
But Jenkins, who has started five of the Lions' last six Test matches on the 2005 and 2009 tours, does not have a release clause in his contract.
And Toulon, runners-up in the Top 14 last season and unbeaten so far this campaign, confirmed through coach Bernard Laporte that they would not be releasing any potential Lions early.
Laporte outlined his hard-line stance ahead of today's scheduled meeting with Gatland, who has flown to France specifically to discuss the thorny issue of player release.
"The international window begins on the weekend of June 9. Everything that happens before that is outside of the window," Laporte told L'Equipe.
"As far as freeing up Gethin, in principle, it's a no.
"If he plays in the final, he will leave the day after, on Sunday June 2, but not before.
"You don't pay a player to be playing with the Lions at the most important moment of the season."
On the day he was confirmed as head coach, Gatland highlighted how Nathan Hines had walked out on Perpignan before the 2009 Top 14 final in order to tour with the Lions.
"Ultimately it may be up to the players," he said.
But Hines was leaving Perpignan anyway that summer.
With Laporte adamant and Jenkins tied to the terms of his deal, Gatland will have to cross his fingers that Toulon do not reach the final.
If they do, the Lions coach would have to soften his stance if he is to have one of the world's leading loosehead props available for the Test series against Australia.
"You don't want to cut your nose off to spite your face in terms of making those players unavailable if they're really, really important for you," Gatland said on Tuesday.
"But I'm also really, really conscious that you want the whole squad together. You don't want people coming out late on a Lions tour - you want them in right from the start.
"If it means us having to make a really, really tough call because someone's not available because they made a decision to go to France, we might have to make that call because it might be the best thing for the squad.
"At the end of the day, it's all about what's best for the team."
It is understood Gatland was not quite so bullish in his meeting with Laporte today, indicating a potential for compromise.
Toulon were appreciative that Gatland took the time to fly down and discuss the situation with them face-to-face.
Gatland will also be meeting Perpignan and Bayonne during his trip to France to talk over the release of players like Mike Phillips, James Hook and Luke Charteris.
It is unlikely that either Perpignan or Bayonne will be contesting the Top 14 title and so Gatland should not face the same issues with them as he does with Toulon.
But Rob Howley, the caretaker Wales coach, has travelled with Gatland and will want to discuss access for the autumn internationals and the Six Nations.
Wales' fourth autumn Test, against Australia on December 1, falls outside of the International Rugby Board's international window which governs the release of players.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.