The 29-year-old has five England caps but has been overlooked by coach Stuart Lancaster since moving to France in 2011 due to Rugby Football Union rules that say overseas-based players will be selected only in extraordinary circumstances.
But British media reported on Tuesday that talks are taking place between leading Premiership clubs and Toulon about signing Armitage.
"The season's begun. We have to be quick if he wants to change," Toulon coach Bernard Laporte told the BBC.
Armitage, who was voted European player of the year last season, signed a three-year contract extension with European champions Toulon in 2013.
"He has a contract (with Toulon), but if the England coach says if he plays for Bath or for Saracens then he will play in the World Cup, I think he has to play for these clubs," he said.
Armitage, whose brother Delon also plays for Toulon, emerged as a target for the French selectors after a change in International Rugby Board (IRB) eligibility.
A move back to England's Premiership would represent a coup for Lancaster, bringing back an important player ahead of next year's tournament and warding off interest from a major rival.
Armitage, a dynamic runner and skilful operator at the breakdown, would compete for the England openside flanker position with captain Chris Robshaw and give Lancaster more strength in depth in a crucial position.
Toulon host Scarlets in the European Rugby Champions Cup on Sunday and if Armitage plays he would be ineligible to represent another club in the tournament.
(Reporting by Sam Holden, editing by Ed Osmond)
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