Mata, who is fit, was not involved with the Blues' session and could sign for United before the end of the week.
United, who will break their transfer record for the 25-year-old Spaniard, are preparing for tonight's Capital One Cup semi-final second leg with Sunderland.
He will become David Moyes' second signing, following Marouane Fellaini's deadline day arrival in September.
The BBC say the Barclays Premier League champions are believed to have tabled a £35 million offer for Mata through intermediaries, and he has told his family he is joining the club, according to the Telegraph.
United experienced a major embarrassment in September when third party "imposters" supposedly scuppered a deal for Athletic Bilbao midfielder Ander Herrera.
Mata joined Chelsea for £23.5m in 2011 and was named the club's player of the season in his first two campaigns.
However, he has featured just 17 times under José Mourinho - 11 of them starts - and has not played since he was substituted at Southampton on New Year's Day.
Last month, Chelsea announced a loss of nearly £50m in the year to June 2013 and have already sold Kevin de Bruyne to Wolfsburg for £18m this month. Nemanja Matić has returned to Stamford Bridge for £21m, but the sale of Mata, who is halfway through a five-year contract, would ease any anxiety about financial fair play.
United's record transfer buy remains the £30.75m they paid Tottenham for Dimitar Berbatov in 2008.Suggest a correction