Frank Lampard hopes Chelsea team-mate John Terry can follow him by signing a new contract with the club.
Argentina striker Sergio Aguero insists he is happy at Manchester City.
The 18-year-old has agreed a deal to keep him with the npower Championship side until 2015 after a successful trial period.
Forrester joined the Toffees' academy aged nine and went on to feature regularly for the Under-16s and Under-18s.
More recently the youngster had been on the fringes of Alan Stubbs' development squad, making seven appearances for the Under-21s this season.