According to French publication L’Equipe, the Blues made an offer of about £27.5 million for Doucouré, 26, who is said to be ‘tempted’ by a new challenge.
But Watford will seemingly demand an extra £10 million before considering letting their French midfielder leave Vicarage Road.
A move for Doucouré by Everton may come as a surprise, with the Blues having already signed two midfielders this summer in Mainz 05’s Jean-Philippe Gbamin and Manchester City’s Fabian Delph.
Though with Muhamed Bešić and James McCarthy on the periphery and Morgan Schneiderlin repeatedly linked with a loan departure to Fenerbahce, Blues boss Marco Silva could perhaps be forgiven for still looking for further reinforcements in this area.
Doucouré is a player Silva is already familiar with, having been a key player in his squad at Watford during his time as Hornets manager from May 2017 until January 2018.
Silva described Doucouré as a ‘high quality player’ before the Blues’ 2-2 draw with Watford in December - a game in which the midfielder scored.
In total, Doucouré has made 92 Watford appearances since joining from Rennes in February 2016, netting 13 goals.