The offer is understood to have been made through a third party, allowing United to stick with their stance of no official bid being made, which remains the case.
It is purely a case of semantics though, with the transfer likely to be completed over the next few days - possibly in time for Mata to make his debut next week, when United host Cardiff on January 28 and visit Stoke on February 1.
Mata is thought to have missed training on Wednesday and is said to have indicated to friends he was destined for Old Trafford.
Although Chelsea are yet to formally acknowledge the bid, still less they accept it, a move for the 25-year-old would make sense from virtually every angle.
Although former United defender Gary Neville pointed out earlier this week his arrival would represent a change of tactic for the Red Devils, who have traditionally relied upon two wingers, the fact none of Antonio Valencia, Ashley Young and Nani have sparkled under Moyes this season means ditching the concept would not be a hardship.
In addition, it would prove to United fans their club was serious about addressing the sharp decline in fortunes experienced since Sir Alex Ferguson's departure, even if it cannot guarantee the Champions League spot they crave.
For Mata, it would end a tortuous few months, where he has left Chelsea boss Jose Mourinho unimpressed and become increasingly marginalised, thereby enhancing his chances of making Spain's World Cup squad.
Chelsea would bank a far larger fee than they could hope to attract from Mata's other suitors - Barcelona and Paris St Germain - and, while it would be unusual for them to sell to a fellow Barclays Premier League giant, Mourinho knows United are not a threat in this season's competition.
Indeed, given United have played Chelsea twice but must still encounter Arsenal and Manchester City in the run-in, it could be argued Mourinho is strengthening his own team's position.
For Moyes, it can only be the start of what is sure to be an extensive rebuilding programme, that is not likely to be completed for another 18 months, with the Scot adamant he is not prepared to rush his work.
"I fully understand that supporters are keen to see us freshen up the squad with new faces, but January is a difficult month in which to bring people in," Moyes told United Review ahead of Wednesday's Capital One Cup semi-final second leg against Sunderland.
"While we are actively scouting players all the time, a lot of the work we are doing now is preparation for the summer.
"If we can do any business now then we will certainly try to do it, but I will not compromise the standards required for a player that can come into this club and help improve it."
The news should fuel an intense atmosphere at Old Trafford, as United look to overturn a 2-1 first-leg deficit.
Yet, from the despair of four defeats in five games since the turn of the year, Moyes can see good times ahead.
"We all know that our club is undergoing changes at present, but I have a clear path in my mind and I know where we are going," he said.