The Merseyside club are thought to be looking to replace Sam Allardyce ahead of next season, but West Ham are also believed to be in the market for a new manager, with David Moyes' future at the London Stadium seemingly uncertain.
The Toffees are believed to have their sights set on former Hull City and Watford boss Silva, and The Mirror reports that Everton players are under the impression that Allardyce will depart the club in the summer, and that Silva will indeed be his replacement.
However, Premier League rivals West Ham are thought to be throwing a spanner in the works, as they too search for a new boss. But it is not just Silva that the Hammers are trying to tempt to London, as the two clubs reportedly share interest in another managerial option.
Everton have been linked to Shakhtar Donetsk's manager Paulo Fonseca, but it is believed that things stalled after West Ham registered interest in the 45-year-old.
Silva was previously scouted by Everton before they appointed Allardyce in November, but the Portuguese boss was still in charge of Watford at the time. However, following his sacking in January, the 40-year-old is reportedly keen to return to the Premier League ahead of next term.
After a tough season, Everton are expected to make a few changes over the summer, with PSV Eindhoven's director of football Marcel Brands believed to be replacing Steve Walsh. And with Allardyce admitting that his future at Goodison Park is unsure, the rumours of a new head coach being lined up appear to have some truth in them.
The English boss is contracted with the club until the end of next season, but he is seemingly starting to believe the speculation himself.
Speaking after Everton's defeat to West Ham on Sunday, Allardyce said, “Contract for next year. Confident? I can’t quite say confident after all the rumours I’m reading in the paper.
“Generally there’s no smoke without fire. We’ll wait and see when we meet up.”
With Fonseca and Silva both thought to be targets for Everton and West Ham, it could be a case of 'we'll have one, you have the other', as the two sides look to land a new boss this summer.