Sean Dyche has prioritised signing a striker this summer after keeping Everton in the Premier League on the final day of the season.
Everton still have a limited budget to work with due to FFP constraints and are accordingly working towards strengthening their squad.
The Toffees have been looking at several strikers across Europe but Toure has emerged as one of the top targets.
And, according to Belgian journalist Sacha Tavolieri, they have moved in with an offer for €40m to sign the striker from Almeria.
The bid is in and they are waiting for an answer from Almeria who are now aware that they are likely to lose the striker.
Everton have also offered him a five-year contract worth €4.3m in gross wages as part of the package.
However, the Toffees are not the only Premier League club who are interested in signing Toure this summer.
It is claimed that Nottingham Forest, Wolves and Fulham are all ready to join the fight for the hitman.
Clubs from Serie A are also interested but they are yet to table an offer like Everton for Toure.