Rennes have accepted a £9.6m offer from Russian club Rubin Kazan for Yann M'Vila, but the France midfielder favours a move to England.
QPR and another unnamed Premier League side have made bids that could rise to £6.6m, while Fulham have indicated they would pay £5.8m.
Rubin have offered M'Vila a four-year deal worth £3.75m a year after tax.
The situation is complicated by M'Vila's ban from international football by his national association.
An unauthorised night out while on France Under-21 duty saw him suspended from all national teams until June 2014.
If M'Vila, 22, can persuade the France Football Federation (FFF) to reduce his punishment - he hopes to find out by this weekend - he will look to boost his international hopes by pushing for a move to England or staying at Rennes, where he is under contract until 2015.
But if the FFF maintains its stance, he may agree a lucrative move to Russia and attempt to reignite his international career once the ban is lifted.
QPR were confident of recruiting M'Vila with a £6.2m offer that would rise by around £400,000 if they avoid relegation, but M'Vila was undecided on signing for the Premier League's bottom team.
He would prefer to join the unnamed club, who would pay £3.3m up front and a further £3m, or £3.3m, at the end of the season.
The English sides are suggesting a salary of around £3m a year, although an issue is Britain's current 50% tax rate. It is due to reduce to 45% in April 2013 but this still compares unfavourably to Russia.
Fulham registered an interest in M'Vila, who has won 22 caps for France, with Rennes in December, but no formal bid has been submitted.
The French outfit's asking price last summer was almost £17m and they reportedly rejected a £28m bid from an English club a year ago.
However, a series of off-field problems have seen M'Vila's stock fall and Rennes want to offload him before the January transfer window closes.
He has made 16 league appearances this season and has helped Rennes to the French League Cup final.