United boss Alex Ferguson was prompted to start talks for Nasri once City declared their interest after losing out on Alexis Sanchez, says The Sun.
Now City are planning the first big move for Nasri, who has a year left on his contract after arriving in a £15.8m move from Marseille three years ago.
But Nasri, 24, has refused to sign a contract extension, demanding assurances that Arsenal are ready to compete again with United and Chelsea by bringing in big signings. But they were not forthcoming.
Arsenal can cash in now - or risk losing Nasri for nothing at the end of next season.