Vignal was offered a three year deal but his agent, Philippe Flavier, says the French defender was not impressed by the terms on offer.
"There has been no progress at all. I think the talks have come to a full stop," said Flavier.
"We met with Rangers for the second time and there was no movement.
We are both very disappointed because he loves playing for Rangers and is very happy with the coach but we have no choice.
"Now I will work with other interests because we have time before May.
"It is not a good ending to a weekend that brought a cup win but Gregory still has a league championship to win and will do his best."