Liuzzi, leader of the Formula 3000 International Championship, has held talks with Ferrari boss Jean Todt, the Independent newspaper said.
Liuzzi is said to have impressed both Todt and Schumacher, with Ferrari ready to offer him a drive for 2005.
That could be as their test driver, or as racer for satellite team Sauber.
Liuzzi has impressed greatly by winning six of this season's seven F3000 races so far.
He also raced against and beat Schumacher in a karting event in 2001.