The Paris Saint-Germain winger, who operates primarily on the left, is surplus to requirements at the Parc des Princes following disciplinary issues and is thought to be keen on a move to England.
Allardyce is no stranger to gambling on players with questionable reputations and looks set to make Rothen his ninth signing of a busy summer at Ewood Park.
The former France international has played his entire career in his homeland but has not ruled out a move to England at the age of 31.
"There have been contacts," Rothan told skysports.com. "I have nothing for the press, but for sure I will play for a club this season, no doubt about it.
"If it is not in Paris, it can be somewhere else."