The Mirror reports that Wilshere is on a five-man short-list of players Real Madrid want to sign by 2014.
Wilshere’s current contract with the Gunners is set to expire in 2014.
The 19-year-old last week pledged to stay with the Gunners for the rest of his career.
Real Madrid are looking to change their strategy from signing proven mega-stars to bringing in Europe’s best young players for fees of around the £25million mark, according to Spanish newspaper Marca.