The French striker signed from Strasbourg in the summer of 2010 but has started just 14 games for the Merseyside club.
He scored in Everton's 5-0 win over Leyton Orient in the Capital One Cup and replaced Kevin Mirallas in the FA Cup win at Bolton on Saturday.
But with his chances limited David Moyes has made the decision to allow him to play first team football.
He is sure to be in demand by clubs in Ligue 1 after netting nine times in just 18 appearances for Strasbourg before his move to Merseyside.
Brest are thought to be the club closing in on the signature of Gueye.
But the identity of his destination club is yet to be revealed.