United have so far been rebuffed in their attempts to bring Fabregas back to the Premier League ahead of the new season, but May believes the former Arsenal captain might fancy the move if Barca's asking price is met.
He told Sky Sports News Radio: "When good players are there it's right that United should go for them. I wouldn't say that they're desperate; Barcelona are holding on to him, and rightly so because he is a good player.
"I think it's down to Cesc at the end of the day. If he feels he's not going to get in front of Xavi and (Andrés) Iniesta then the move to United would be perfect for him."
May also feels that United should knock back any approaches for unsettled striker Wayne Rooney, with time running out to find a replacement before the transfer window shuts in five weeks' time.
"To lose Wayne would be losing probably 20 goals next season and you're going to run out of time [to replace him], with forwards at a premium.
"If we do get rid of Wayne or if he decides to leave then we've got to replace him. Clubs out there don't want to lose their best players."
You can hear May's full interview, in which he also talks about United's pre-season campaign, here.
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