"The move is subject to the Egyptian international agreeing personal terms and completing a medical," the London club said on their website (www.chelseafc.com) on Thursday.
"The winger scored against us twice in the Champions League earlier this season and impressed against the Blues in last season's Europa League semi-final."
Chelsea beat Basel over two legs in the Europa League before going on to defeat Benfica 2-1 in the final in Amsterdam in May.
The transfer fee for Salah was undisclosed but media reports speculated that he could cost up to 16 million pounds ($26.61 million).
The 21-year-old will occupy one of the three attacking midfield positions behind the sole striker in manager Jose Mourinho's preferred 4-2-3-1 formation.
Salah faces a tough test dislodging Mourinho's first-choice trio Eden Hazard, Willian and Oscar who have featured in Chelsea's sparkling run of six successive victories in all competitions.
Mata, the London club's player of the year for the last two seasons, has been out of favour under Mourinho this term and has not featured since being taken off in the 3-0 New Year's Day victory at Southampton.
According to media reports, Chelsea have accepted a bid of 37 million pounds from United for Mata, who has accepted personal terms with the Premier League champions and is due to undergo a medical later on Thursday.
Liverpool had also been strongly linked with a move for Salah who will hope to complete his transfer in time for Sunday's FA Cup fourth round tie against Stoke City at Stamford Bridge.
It will be Chelsea's second major deal of the January transfer window after they re-signed their former holding midfielder Nemanja Matic from Benfica last week.
Matic came on as a second-half substitute in third-placed Chelsea's 3-1 home league win over United on Sunday.
($1 = 0.6013 British pounds)
(Reporting by Tony Jimenez; editing by Pritha Sarkar and Toby Davis)
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