The 23-year-old only moved to the San Siro last January from Bayern Munich but the Daily Mail claims that Inter are looking to restructure their squad this summer and contemplating selling of a number of key players.
The report suggests that Everton have made enquires to Shaqiri's former clubs - Bayern and FC Basel - about his character to assess whether he would fit into the squad.
His performances on the field suggest he will have no problem adjusting to life at Goodison. The midfielder has nearly 50 caps for Switzerland having represetned them at every youth level.
He has also won 13 major honours during his career, including two Bundesliga titles, the Champions League, Super Cup and World Club Cup.
Whether he would be tempted to leave the bright lights of Milan though is another question - Everton may have to pay big money to lure the midfielder across to England.