The Blues are pushing ahead with their summer business having already completed the signings of Jordan Pickford, Davy Klaassen and Henry Onyekuru.
Chief among their priorities is finding more attacking players to help spread the goals around the team having relied heavily upon Romelu Lukaku in that department last season.
That has led Ronald Koeman and Steve Walsh to assessing a number of potential targets across Europe, especially if Lukaku ends up departing in a £100m move to Chelsea.
Sandro Ramirez has already been signed from Malaga, with his move to be finalised on Monday, but he is unlikely to be the only forward targeted.
According to Joyce, Arsenal striker Olivier Giroud is also on the list of possible targets. He reports that the Blues believe a £20 million bid could be enough to secure the 30-year-old’s signature.
The Frenchman could find himself further down the pecking order this summer as the Gunners push hard for Lyon’s Alexandre Lacazette.
With Alexis Sanchez, Theo Walcott and Danny Welbeck also in the squad, that would his chances of a starting role slim at best.
Everton could look to exploit that by offering guaranteed first team football at Goodison Park, something that will be crucial to Giroud if he intends to make it into France’s squad for the World Cup next summer.