The Toffees' dismal continental campaign, which has seen them pick up just one point from their five group games, ends against Apollon Limassol in Cyprus, where Shakespeare and fellow first-team coach Duncan Ferguson will be in the dugout due to Sam Allardyce's absence.
Everton can not qualify from Group E after what has been nothing short of a disastrous European venture this season.
Wayne Rooney, Gylfi Sigurdsson and Jordan Pickford are among them, with Allardyce conscious of Sunday's Merseyside derby, and Schneiderlin's presence on the other side of the continent could be interpreted as a reflection of his place in the Goodison Park pecking order.
The French worldwide will be one of Everton's most experienced players against Limassol, with numerous Toffees youngsters set to start.
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Buyers from the Middle East and Asia have been snapping up masterpieces to fill regional museums - and pushing prices ever higher. The organization behind the museum became one of the most aggressive buyers on the global art market over the last decade.
Assistant manager Sammy Lee and first-team coach Craig Shakespeare will oversee the match in Cyprus instead, as a skeleton Everton side face off against their Cypriot opponents in what Allardyce previously termed a "dead rubber" match for both clubs.
"I have come here, I know my role, my responsibilities, I want to try and improve the players, try to improve the football club, improve myself as well. I have no problem with it, of course, when the game is going on you can get wrapped up in the situation but I'll get some clarity on that".
Allardyce oversaw a 2-0 victory in his first match at the helm on Saturday as Everton saw off Huddersfield Town to climb into the top half of the table for the first time since August.
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