The United left-back has been linked with Monaco and Paris Saint Germain but the report claims Inter Milan have made the first move for the 32-year-old.
Representatives from the club reportedly spoke to Evra's agent about whether he would be keen to join the club in the summer, although no contract offer was made.
While the opportunity to return to finish his career in France may hold some appeal for Evra, Inter Milan may be able to offer him the chance to continue to play alongside Nemanja Vidic.
The United captain has confirmed that he intends to leave Old Trafford at the end of the current campaign, and Inter Milan are thought to be the frontrunners to sign him up.
Evra is believed to be keen to get a fresh start after eight successful years with United.
The France international joined United from Monaco in 2006, and the big spending French club are thought to be interested in bringing Evra back to Ligue 1.
The left-back remains a first-team player for David Moyes, so were he to leave the United boss would likely have to bring in a replacement.