The Toffees are expected to spend big this summer, with manager Ronald Koeman promised big funds by shareholder Farhad Moshiri.
The Toffees have been linked with a number of players as a result, but so far only goalkeeper Maarten Stekelenburg has arrived from Fulham.
One man they have been linked with is Sporting Lisbon midfielder William Carvalho, who was a star performer for Portugal as they won Euro 2016 earlier this summer.
And according to the Mirror, the Blues are leading the race for his signature, but now face competition from Chelsea for him.
They report that Blues boss Antonio Conte wants to sign another midfielder after completing a move for N’Golo Kante.
He has been frustrated in his attempts to sign Radja Nainggolan from Roma and so has turned his attention towards William instead.
Whether he would be interested in either club remains to be seen though, with neither able to offer him the chance to play Champions League football next season.