The Everton boss is said to have held a meeting with owner Farhad Moshiri recently, where he was told that the pressure was on.
However, Silva is set to be in charge at Everton for at least the next three games.
The Toffees want to give Silva a chance to turn things round at Goodison Park, despite their awful start to the season.
Everton are currently sat in 18th place in the Premier League table with their performances, particularly in an attacking sense, failing to impress.
Silva is said to be ‘confident’ that he can arrest his side’s slide, and improve their form but he is running out of time to do so.
A range of candidates have been linked with the job at Everton, but it is claimed that a shortlist to replace Silva still has not been drawn up.
Moyes, therefore, has not been contacted with Everton, with the board still backing Silva at this stage.
Everton’s next three games come against West Ham United, Brighton & Hove Albion and Watford.
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