The Hornets issued a hands-off warning after the managerless Toffees made an approach on Monday.
It is also claimed that Silva is happy at Vicarage Road and is not interested in heading to Everton where the pressure will be on nearly immediately.
It's now been three weeks since Koeman became the third Premier League casualty of the season - West Ham have since sacked Slaven Bilic - and yet the struggling club remain managerless.
Hornets boss Silva has forged an impressive reputation for himself since arriving in England less than a year ago as a relative unknown.
The Portuguese nearly pulled off a miracle by keeping Hull in the Premier League last season before switching to Watford, where he has also started well.
Despite having suffered a dip in form, losing their last three consecutive matches prior to the global 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.
Watford are not prepared to allow Silva to leave mid-season and are unlikely to face any resistance despite the 40-year-old's willingness to hear Everton's offer.
The former Everton defender now looks set to still be in charge for Saturday's trip to Crystal Palace.
Despite the rejection Silva remains the favourite at the top of the Next Everton Manager Market, ahead of David Unsworth and Sean Dyche, but you can bet your last penny that Everton will try their luck again.