The Sun says the Portugal winger is a shock £20million target for Arsenal.
The winger is in a contract row with Manchester United and could leave next month.
Arsenal are looking for a quality replacement for Theo Walcott, whose future at the Emirates looks bleak.
United want significantly more than the £14m they paid to Sporting Lisbon in 2007 and Arsenal boss
Zenit St Petersburg and Paris St Germain have also been watching Nani but he would prefer to remain in the Premier League.
Chelsea are also keeping an eye on the wideman.