The Belgium international picked up a knock in the victory over Stoke, but his manager is hoping he will be able to shake off the injury in time for the trip to White Hart Lane
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.