Wenger will make a move for the French youngster in the January transfer window, according to News of the World.
The 19-year-old defensive midfielder has been the target of growing interest from Manchester United and Tottenham in recent weeks.
Schneiderlin joined the Saints from Strasbourg and Wenger was prepared to wait until signing the youngster, but with the growing interest from other Premier League clubs he has decided to make a January move.
Reports also suggest Fulham are ready to make a £5million offer for the France Under-19 captain.