The French defender has lent his support to the Scottish manager despite an underwhelming season, while he could be forced to "study the possibilities" of a move away.
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A miserable season for the Old Trafford outfit was compounded by a 2-0 loss against Olympiakos in the first leg of the Champions League last-16 tie, but Evra insists Moyes retains the full backing of the squad.
"There was a big change, nobody likes change," the defender told French radio station RMC Sport, acknowledging the impact made by Ferguson during his lengthy tenure at Old Trafford.
"We are behind the new manager. We will do everything to qualify for the next Champions League, my love for the club will not change."
As reported by Goal, Evra is being targeted by Inter as the Italians look to bolster their back line, but the Frenchman revealed he had not considered his future at Old Trafford yet - though could be forced to consider his options.
"I love Manchester," he added. "When my love is broken with Manchester, I will study the possibilities.
"Everyone respects me, I feel at home here. It's beautiful. I have very good relations with the new coach."