Lyon have challenged Paris Saint Germain's resolve to sign Jeremy Clement this month.
The Rangers midfielder is keen to return to Ligue 1 after just six months in Scotland.
Former Ibrox boss Paul Le Guen is hoping to bring him to PSG, but Gerard Houllier has also entered the race.
Lyon chairman Jean-Michel Aulas is believed to have made a é¼2.6million (£1.7million) bid to the Scottish giants, topping PSG's offer of é¼2million (£1.3million).
Rangers now want the Parc des Princes club to match Lyon's offer, with Clement preferring a move to Paris.
Clement left Lyon in the summer having failed to secure regular first-team football and is understood to be surprised by the French champions' desire to re-sign him.
Meanwhile, Lyon are rumoured to be readying a bid for Auxerre captain Benoit Cheyrou.
The midfielder has been with Auxerre for the past two-and-a-half years but could be attracted by the prospect of UEFA Champions League football at the Stade Gerland.