Roberto Martinez has confirmed he intends to given Seamus Coleman and Muhamed Besic as long as possible to prove their fitness ahead of Saturday's trip to Swansea.
Both players became the latest victims of Everton's hamstring curse last weekend against Chelsea, though Besic's early withdrawal did result in the introduction of hat-trick hero Steven Naismith.
Coleman limped off midway through the second half and was replaced by Ramiro Funes Mori, who could be in line to start at the Liberty Stadium should the Ireland international not recover in time.
Martinez is refusing to rule either player out though after confirming they had responded well to initial treatment at Finch Farm this week.
Speaking at his pre-match press conference, Martinez said:
"We've had positive news on both because [the injury] is the least we expected in terms of soft tissue injuries and they're both reacting well to treatment.
"It's difficult to tell when we will be able to get them back but I would give both a chance to be involved at the weekend or Tuesday in the League Cup.
"Apart from those two, everyone is fit and available from the squad that faced Chelsea and all the other players are doing well."
Meanwhile, Bryan Oviedo and Darron Gibson could make their return from injury against Reading in the League Cup on Tuesday.
Oviedo has been out for the past fortnight with a knee injury that forced him to pull out of the Costa Rica squad during the international break.
Gibson hasn't played since March due to a persistent foot injury, though there is also the small matter of a drink-driving conviction earlier this month that has blighted his rehabilitation.
Speaking of the recovering duo, Martinez added:
"Bryan will probably be ready for the League Cup game. Darron is a just a matter of fitness now. He played over 70 minutes at Goodison on Monday, so clearly he is on the road to regaining that match fitness.
"Medically, he's fully fit and ready to rejoin the group, it's just a case of getting him that match fitness."