The Italian has previously expressed a desire to remain in England.
Crotone have been promoted to Serie A next season whilst Empoli finished in 11th place in Italy’s top-flight this season.
If Macheda did make the move it would be his first return to Italy since heading to Sampdoria on loan from United in 2011.
The former Italian under-21 international is reported to not be keen on a move to Italy as the report claims he may see it as a step backwards.
Macheda only joined Cardiff on a free transfer last summer after impressing on loan at Birmingham City. However, he struggled to make an impact with The Bluebirds and spent an uneventful spell on loan at Nottingham Forest toward the end of the Championship campaign.
Macheda’s contract at Cardiff expires next summer but it will remain to be seen if the club’s new head coach wants him as part of the first-team plans, after Russell Slade moved upstairs.