The 31-year-old, who is out of contract at Ewood Park next summer, has made just 14 appearances this season after falling out of favour at Rovers.
He was linked with a return to France in January with Evian but a move failed to materialise.
Givet admits he has found things difficult at Blackburn since their relegation to the Championship last year and is hoping to return to his homeland.
He told L'Equipe: "I am eager for the season to be over, to go on holiday and to take stock.
"If I have a good opportunity I would like to go back to France. I miss France and I still want to play."
Givet added of previous interest from other clubs: "When the club was relegated to the Championship I had chances to leave, but the club asked for €3-4million.
"This winter, there was Evian TG. But the officials told me: 'If you leave on loan, you give up your last year of contract.' Impossible! What happens if I get injured? The club makes me pay for the past."
Givet, who arrived in Lancashire in 2009 from Marseille, admits the club's slide into the second tier has left him unhappy after seeing his playing time become limited.
"The first two or three years, it was just great," he added. "I had great fun in Premier League.
"Then, the club was relegated. I thought I would leave, but it was not sorted out.
"Being in the Championship was difficult to experience, especially as I didn't play. Frankly I was depressed. It was very difficult.
"I am not the kind to cry, but I questioned myself a lot. It wasn't fun anymore. When everything goes wrong on professional level, everything is dark. You think 'what am I doing here? It is raining 28 days out of 30. The food is not good...'
"You want to go back to France in your village in South of France with your friends and family."