The France international is believed to be among a group of experienced heads United are prepared to part with this summer.
Nemanja Vidic has already confirmed that he will be leaving Old Trafford at the end of his current contract, and fellow centre-half Rio Ferdinand could be joining him.
Evra finds himself in a similar situation after seven years with the Red Devils.
Inter Milan, who are reported to have agreed a deal with Vidic, are among those closely monitoring his situation, along with wealthy Ligue 1 outfits Paris St Germain and Monaco.
Evra is, however, remaining coy when it comes to his next move, insisting that he will only explore his options when a love affair with United is 'broken'.
He told RMC Sport: "My love will not change for the club.
"I love Manchester. When my love will be broken with Manchester, I will study the possibilities.
"I am only thinking about the present. In May I will be 33 years old. I really want to have fun at the next World Cup, enjoy every moment and give my all."
Evra has also been discussing the changes at United which have led to them struggling for form in 2013/14, with David Moyes yet to convince as successor to the legendary Sir Alex Ferguson.
"There was a big change, it must be digested - nobody likes change," added Evra, who was snapped up from Monaco by Ferguson in January 2006.
"The team played for over 28 years with Alex Ferguson.
"It is behind the new manager, we will do everything to qualify for the next Champions League."
United currently sit 11 points adrift of the top four in the Premier League table and suffered a 2-0 reversal in the first leg of their last-16 showdown with Olympiakos in this season's Champions League.