The Toffees chief has been strongly linked with a move away from the Premier League in recent times, with contract negotiations between himself and the Merseyside club stalling.
The Scot is believed to be waiting until the end of the season before making a decision on his future, but some have suggested that he could be tempted by a new challenge.
Although it is far from certain that Moyes will walk away from Goodison Park, he is thought to be extremely keen to hear Schalke’s proposal.
He is said to have concerns regarding Everton’s long-term ambitions, with the club currently in the race for Champions League football.
Moyes wants to test his abilities on the top stage, but knows that if top players are sold and investment in the squad not allowed, he is unlikely to achieve his aims on Merseyside.
He has been suggested as a possible replacement for Sir Alex Ferguson at Manchester United, however there are rumours that he is keen to move abroad to further his coaching development.
If Moyes does move on, Everton could turn to Celtic boss Neil Lennon.
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