Media reports on Tuesday morning suggest the Red Devils are preparing a bid for the Spanish attacking midfielder, who has spent most of this season on the sidelines at Stamford Bridge.
Mata’s most recent of his 13 Premier League appearances this campaign, against Southampton on New Year's Day, ended with the 25-year-old reacting angrily to being substituted.
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Former United right-back Neville, though, told Sky Sports he cannot see where Mata would fit in unless David Moyes is planning an overhaul of the squad.
"The first question, I think, is where are you going to play him? Wayne Rooney and Robin van Persie are up top if they are fit so where are you going to play him? Are you going to play him off the left or off the right?
"That's a lot of money, 37 million quid, but they need a signing.
"Does he fit with what I would call the typical philosophy of Manchester United? I would say no.
"Maybe they have to change the philosophy and maybe that's what David Moyes is thinking. Maybe he wants to play narrow wide players and maybe a three in midfield.
"They would have to change to accommodate Juan Mata in the way they normally play. They normally play with wide players. Sometimes they tuck in, but generally they have wide players and the thing for me is where is he going to play?"
On Tuesday morning, Neville attempted to clarify his position by posting on Twitter: "My quote - 'Does he fit with what I would call the typical philosophy of Manchester United?' I would say no. Not he won't fit.
"Positives of signing a player like him are obvious- lift everyone (spark), creativity, knows PL (Premier League), 4th place chances go up - fantastic player."
"They need to sign a big player," he added. "They need to make a noise and if they get him in it will attract other players - and they need three or four players.
"What it could be is the start of something to lead to other things, but typically I wouldn't say [Mata] fits."