Watford value him at around £40 million but, according to L'Equipe, Everton are set to make a third bid.
The report adds that Silva is an 'enormous' fan of the 26-year-old, who played under the Portuguese manager at Vicarage Road.
Everton won't be able to sign him this month if Thursday's transfer deadline passes without Doucoure being on Merseyside, but the report also claimed that interest could be renewed in January.
It's been an excellent window for the Goodison Park club, who spent £29 million on signing former Juventus hitman Moise Kean a few days ago.
Kean was the fifth senior player to arrive this summer, following Jean-Philippe Gbamin, Fabian Delph, Jonas Lossl and Andre Gomes.
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