Everton are continuing their search for a new manager following the sacking of Ronald Koeman and Silva has emerged as one of their top targets.
Interim boss David Unsworth will take charge of his fifth game as Everton travel to South London for a vital clash with fellow strugglers Crystal Palace on Saturday.
Renewed contact between the two parties was made on Sunday but Allardyce felt the contract on offer from the Merseyside club - running only until the end of the season - was not enough to tempt him out of retirement.
White also added that Silva would in fact have been interested in speaking to the board at Goodison Park if a deal was to have been reached between the sides, but that Watford knocked back the approach without a second thought.
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Unsworth's side ended a run of bad form just before the global break when they came from 2-1 down to beat Silva's Watford 3-2 at Goodison Park.
Everton parted company with Ronald Koeman back in October and have been on the lookout for a new manager ever since, with Sam Allardyce's name mentioned in connection with the role prior to the current worldwide break.
The Hornets do not wish to entertain any further approaches as they are adamant they can not lose a coveted manager halfway through a campaign.