The midfielder has one year left on his contract with the Premier League club, however, it has been speculated that boss Arsene Wenger has grown tired of the Czech's regular injury and illness problems.
Rosicky, though, has had his tonsils removed this summer because doctors believed they were the cause of numerous viral infections which have limited his availability for selection.
And, unlike Fabregas, who has been wanted by Barcelona for several years, and Manchester City targets Samir Nasri and Gael Clichy, the 30-year-old has pledged his commitment to Arsenal after receiving assurances from Wenger.