The Frenchman is entering the final year of his Black Cats contract and with manager Steve Bruce having made nine signings to date, a transfer has been mooted.
"I'm very happy at Sunderland and I do not want to leave this club," Malbranque told The Journal.
"I want to stay and fight for my place, I have no interest in leaving and would like to stay as long as possible.
"The club has moved forward every year I have been here and we have to do it again."
Malbranque joined Sunderland in 2008 from Tottenham Hotspur.