Emirates officials could now face another row with a Spanish club, following constant battles with Barcelona over their chasing of Thierry Henry and Cesc Fabregas.
Wilshere, 19, currently sidelined by a foot injury, signed a new five-year Gunners contract last year and has pledged his loyalty.
But Real are fed up with paying massive sums for stars at the peak of their careers. Cristiano Ronaldo cost £80million.
Instead, they want to sign a group of youngsters for between £20m and £30m and hope to bag all five by 2014.
Listed with Wilshere in Spanish sports paper Marca - closely linked to Real - are Barcelona B midfielder Rafinha, Athletic Bilbao winger Iker Muniain, Lille playmaker Eden Hazard and Dortmund midfielder Mario Gotze.