Recent speculation had suggested that Italian side Livorno were keen to sign the 31-year-old.
However, despite the fact that the Frenchman was left out of the Rovers squad that travelled to Portugal for pre-season training, he did feature in a friendly against Fleetwood Town earlier this week.
"I am unaware of that. Gael played this morning so that's news to me. Gael was fine today," Bowyer told the Lancashire Evening Telegraph.
Givet joined Blackburn from Marseille in 2009.