The Senegalese centre-half was reported to be attracting interest from the Premier League, with the Black Cats believed to be keen.
Ligue 1 giants Marseille and Lyon were also understood to be weighing up summer raids, as they attempt to bolster their respective backlines.
Mangane has, however, opted against a move elsewhere and has committed his future to Rennes until the summer of 2014.
Upon agreeing fresh terms, the 28-year-old said: "I am delighted to stay with Rennes until 2014.
"I thought about things for a long time and I think I have made the right decision. Rennes are a fantastic club.
"They are not Lyon, with all the glamour and the big business, but they are the ideal club for me.
"I am 28 now, I have reached my peak and I need to prove again this season that I can maintain those standards."