Ligue 1 club Evian are believed to be keen to offer the former France international a two-year deal.
The 31-year-old has played over 100 games for Rovers but is out of contract in the summer and would consider an Ewood Park exit.
"To return to France could be a blessing," said Givet.
"Nothing has been decided yet but my contract expires in June 2013.
"Blackburn have not said anything to me yet so let's wait and see."
The left-sided player joined Blackburn from Marseille in 2008 having won 13 caps for France in his days at Monaco.
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar