Wales' Gareth Thomas and Stephen Jones are likely to be left behind when the Lions fly to New Zealand on 25 May. Both players are wanted for important club matches in France on the final weekend of May.
Lions coach Sir Clive Woodward told BBC Wales Sport he will talk with the clubs this week to reach a compromise.
"Sometimes you've got to sit back and work with the clubs, so possibly those two players may be coming out a week later," said Woodward.
"The professional game has moved on; the Lions series is all about the Test matches.
"We've got to speak to the two clubs but also common sense has got to come into this."
The final fixtures of the French Championship are played on 28 May before the league's top four clubs fight for the title in a play-off system.
Clermont Auvergne, home of Wales fly-half Stephen Jones, have little chance of qualifying; but Thomas' side Toulouse are very much in contention.
The Heineken Cup semi-finalist lie third with five games to go, but Thomas is unlikely to stay behind for either the play-off semi-final (4 June) or final (11 June).
Jones admitted he felt he was "caught between a rock and a hard place", while Thomas is said to be pleased the matter will be settled amicably.
"Naturally Sir Clive would prefer that Gareth was there from the start of the tour," said Thomas' agent Peter Underhill.
"But he will not penalise Gareth for not being there and his selection will be decided in the same way as any other player.
"Clive has been very helpful and very friendly."
The pair will miss the Lions' opener in New Zealand against Bay of Plenty on 4 June, and they are unlikely to feature in the warm-up match against Argentina in Cardiff on Monday, 23 May.
MMIX
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We are caught between a rock and a hard place
