Nani's future at Manchester United is clouded with Aston Villa winger Ashley Young set to sign.
The Telegraph says Nani may now find his opportunities increasingly scarce after seemingly falling out of favour towards the end of last season, with manager Sir Alex Ferguson preferring both Ji-Sung Park and Antonio Valencia in May's Champions League final.
Juventus and both AC Milan and Inter Milan are believed to be tracking the former Sporting Lisbon player.
Nani has expressed an ambition to play for Jose Mourinho at Real Madrid.