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He made 21 appearances across all competitions before suffering a serious knee injury while playing for Ghana at the Africa Cup of Nations in January.
The Toffees and Schalke have reportedly enquired over the possibility of landing him in another temporary switch.
But both clubs are said to now be on the verge of pulling out of a deal after Rahman's return date was pushed back until after the start of pre-season training.
Rahman joined the Blues from Augsburg for £14m in 2015.
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He made 23 appearances for the club before being allowed to join Schalke last summer.
The news of his setback could come as a blow to Ronald Koeman.
He is expected to considerably bolster his Everton squad ahead of a Europa League campaign next term.
He guided the Toffees to a seventh-place finish in his first season on Merseyside.