Willian, who scored in Chelsea's 3-1 win over Manchester City, has only just returned to the fold after he was granted time off to mourn the loss of his mother.
The Brazilian winger, who only signed a new contract with the Blues over the summer, which will keep him at the club until 2020.
Manchester United are currently scouring the market for a midfielder.
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Mourinho previously expressed an interest in Nemanja Matic, and it was thought he could make a move for Willian.
But according to Goal, Mourinho is set to be disappointed.
A source rubbished such claims, indicating 'there is nothing in it'.
Meanwhile, United could see Memphis Depay and Morgan Schneiderlin leave in January.
Everton are thought to be hopeful of completing a double swoop, with reports suggesting terms were discussed for the pair before the two sides met at Goodison Park on Sunday.