Mirallas scored the only goal of the game during their 1-0 victory over Stoke last weekend, but was forced off the pitch with a groin injury ten minutes from time.
The Toffees are now hoping the player will be able to shake off the injury in time to compete in a game which could have such a vital impact on the Champions League ambitions of both sides.
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The Everton manager is already without Marouane Fellaini and Steven Pienaar who complete the final game of their two-match suspensions, but Moyes is hoping the club can continue to pick up points in their absence.
He continued: "Unfortunately we don't have Marouane Fellaini and Steven Pienaar and that would be a blow to anybody's team.
"We found a way of getting a result against Stoke City and it's a bit the same against Tottenham - we're going to have to find a way to get a result without two really key players."
Tottenham have injury concerns of their own, with Aaron Lennon, William Gallas and star man Gareth Bale ruled out for two weeks.