Bordeaux have warned Rangers they would have to double their offer to have any chance of landing Julien Faubert.
Julien Faubert has been with Bordeaux for three years
Reports claim that Walter Smith is ready to table a bid of around £5m for the 23-year-old France midfielder.
But Bordeaux bosses insist they would want more money - even if Faubert was for sale.
Bordeaux chairman Jean-Louis Triaud told the Daily Record: "We don't want to sell him but even if we did agree to sell, £5m would be too low."
Triaud continued: "We do not have a fixed price for him but it would have to be double the kind of money that is being talked about.
"We have never discussed the transfer of this player with Glasgow Rangers."
Faubert's agent plans talks with Bordeaux this week over the France winger's future after Rangers and Tottenham expressed an interest.
"A lot of clubs want to sign him," representative Philippe Sol told the Sunday Mail. "Roma would like Julien, as would Tottenham.
"But a move to Spurs would depend on if they keep Pascal Chimbonda.
"Rangers have shown the biggest interest and the passion to sign Julien is something that attracts him."
Bordeaux chairman Triaud was quoted in the News of the World, insisting that Rangers had not been in touch with his club.
But Sol said: "Rangers are very interested in signing Julien. A move to Scotland is something that excites him.
"His long-term goal is to play in the English Premiership, but playing at a huge club like Rangers could help him achieve that."
Rangers have made no contact, officially or unofficially, with us over Julien Faubert
Bordeaux chairman Jean-Louis Triaud
The link with Rangers was first reported by French newspaper L'Equipe, which suggested that Faubert would follow striker Jean-Claude Darcheville from the French club to Ibrox.
It was suggested that Rangers would pay £4.3m for the 23-year-old, who joined Bordeaux from Cannes in 2004, and that he would sign a four-year contract with the Glasgow club.
However, while Darcheville was a free agent and in the latter stages of his career, Faubert is under contract until 2011 and has just broken into the international set-up.
The winger made his debut for France in August against Bosnia, scoring a last-minute winner to secure a 2-1 victory.
"The fact that Jean-Claude Darcheville is also at Ibrox is important because it could help him settle quickly," said his representative.
"Now we have to find out what Bordeaux want to do with Julien.
"He's an important player for the club and they won't want to lose an international who's on a long contract.
"We will be holding talks this week to try to reach a solution."
A lack of width has been earmarked as a problem by Rangers manager Walter Smith since he took over from Paul Le Guen during last season.
But the Scottish Premier League runners-up are also reported to be close to signing USA international DaMarcus Beasley.
The PSV Eindhoven winger is a similar kind of player and Bordeaux have played down reports of Rangers' interest in Faubert.
"Rangers have made no contact, officially or unofficially, with us over Julien Faubert," said Triaud.
"And, since they did so when they had no need to when signing Jean-Claude Darcheville on a free transfer, I'm sure they would have done so in this case if they were interested.
"It's more likely an agent trying to stir some interest.
"Julien is a player we want to keep in any case."