Spurs looked set to capture the signature of the Brazil international in a move that would see him become their third club-record deal of the summer, following deals for Roberto Soldado and Corinthians midfielder Paulinho.
However, a late €37 million bid (£31.6m) lodged by rivals Chelsea on Thursday added competition for his signature and Mourinho now believes the player has chosen a move to Stamford Bridge instead.
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"I am happy with my squad but every one of us says we are happy. We always want something more and never close the door."
The 25-year-old travelled to Tottenham’s Enfield Training Centre to complete a medical on Wednesday, despite not having signed a contract with the north London club.
Mourinho believes Spurs acted with "danger" by performing a medical before the deal was complete, but denied speculation that any move for the midfielder would force Spain international Mata to leave the club.
"That's the danger of medicals before contracts," he continued, when asked about Willian’s potential move to White Hart Lane.
"I want a 22-player squad. If somebody comes, somebody leaves. We don't need to sell. Loan probably – yes.
"He [Mata] is a player we all like, a player we all want to keep. We want more quality, not less quality."