Watford immediately rejected the unwanted enquiry for their highly-rated boss insisting publicly yesterday that Silva is staying put at Vicarage Road.
His club are in line to be promoted to the Premier League next summer and lead the Championship standings after taking 35 points from 16 games.
The Goodison Park hierarchy had hoped to install Koeman's permanent replacement in time for their first game after the worldwide weekend.
The 40-year-old joined Watford after leaving Hull at the end of last season.
Despite having suffered a dip in form, losing their last three consecutive matches prior to the worldwide break, the Hornets now find themselves in ninth place, six positions and four points ahead of Everton, who have endured a nightmare start to the campaign.
Silva would be a good option for Everton but the fact he has only signed for Watford just several months ago mean that this deal would be very hard to get over the line.
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Silva is reportedly one of the managers on Everton's radar as a result of getting Watford to play an impressive brand of football this season.
They could instead hand current caretaker David Unsworth more time before reassessing their situation in the summer.
Everton are now out of the relegation zone after their win over Silva's Watford side ahead of the worldwide break.
The former Everton defender now looks set to still be in charge for Saturday's trip to Crystal Palace.