In the wake of stories suggesting an approach for the Spain international was imminent, United have denied making a bid.
However, with almost two weeks left before the transfer window closes there is still time for United to possibly try and make the kind of addition many fans have been crying out for.
During his commentary of the Red Devils' 3-1 defeat at Chelsea on Sunday, Neville outlined a view that his old club needed at least three players to lift flagging morale, but in the difficult January window, getting them would be virtually impossible.
Mata's desire to cement a place in Spain's World Cup squad, having failed to secure a regular starting berth under Jose Mourinho at Stamford Bridge, may make the situation far easier in his case, even if Chelsea, rebuffed twice in their attempts to sign Wayne Rooney last summer, may wonder why they should do business with the Old Trafford club.
It has been suggested Neville does not believe it is a good idea either.
However, in a series of Tweets this morning, England's assistant coach has clarified his view.
On Sky's Monday Night Football show, Neville outlined why he felt Mata's arrival would not immediately fit with the manner in which United generally approach their transfer business.
He said: "The first question, I think, is where are you going to play? 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?
"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.
"They need to make a noise and if they get him in it will attract potentially 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 he fits."
With a blank weekend following Wednesday's Capital One Cup semi-final second-leg with Sunderland, Moyes is expected to embark on a scouting mission in an effort to bolster a squad languishing in seventh spot, and in danger of failing to qualify for next season's Champions League.