Shares in M6 opened around 10% higher on the Paris stock market and were up 6.4%, at around 15 euros, at 0714 GMT.
Bloomberg News reported on Sunday French media mogul Stephane Courbit and his investor partners are said to have offered 20 euros ($19) a share.
Reuters on Friday reported a consortium of high-profile French entrepreneurs including billionaire Rodolphe Saade, Courbit of TV production group Banijay and investor Marc Ladreit de Lacharriere was in pole position to clinch a deal.
Italian broadcaster MediaForEurope, meanwhile, joined forces with French billionaire Xavier Niel with a view to a rival bid.
(Reporting by Tassilo Hummel, Editing by Louise Heavens)