Mata, 25, had been the subject of intense speculation in recent days and failed to report to training on Wednesday, with numerous news sources - including Press Association and BBC Sport - reporting that United made an approach on Wednesday.
And the Daily Telegraph has now reported that an offer of £37m has now been accepted by Chelsea, with Jose Mourinho himself sanctioning the sale. "The scale of United’s offer is too big to refuse given his priorities in strengthening his team lie elsewhere," reports the Telegraph, adding that Chelsea already have plans in place for his replacement - rumoured to be Liverpool target Mohamed Salah of Basel.
The player will have a medical on Thursday with a transfer to be finalised over the next few days, with Mata is in line to make his debut next week when United host Cardiff on January 28.
The Spanish star, who Chelsea signed from Valencia for £23.5 million in 2011, is said to have indicated to friends he was destined for Old Trafford.
Although Chelsea are yet to formally acknowledge the bid, still less accept it, a move for the 25-year-old would make sense from virtually every angle.
The Spaniard, who has was voted Chelsea’s player of the season in each of his first two years at the club, has struggled to break into the Blues' side since Jose Mourinho's return to Stamford Bridge, with the Portuguese manager favouring the attacking midfield trio of Eden Hazard, Oscar and Willian.
Yet Mourinho has repeatedly insisted that he wants to keep Mata at the club - despite the player's furious reaction when he was substituted on New Year's Day at Southampton.
Mourinho said after the incident that he wanted Mata to stay, though he did add that any player is free to ask for a transfer if they wish to leave.
United continue to be linked with a host of players as David Moyes seeks to overhaul his squad after a disappointing start to the season.
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 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.