However, after prevailing 2-1 to reach the last four of the competition, his position for now appears to be safe.
Mourinho has been widely fancied to replace the Dutch tactician, and is even thought to have agreed a verbal contract.
But according to the Daily Telegraph, Paris Saint-Germain are prepared to swoop for Mourinho should they dispense with Laurent Blanc.
The French champions were dumped out of the Champions League last night by Manchester City and it is thought Blanc's position will be reviewed at the end of the season.
Blanc only signed a new two-year deal with the Ligue 1 giants in February, but it is believed they will make a third bid for Mourinho, who has rejected their overtures in the past.
Mourinho is already understood to have given United a deadline to complete a deal.
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