Jospeh Yobo and Yakubu Aiyegbeni are hoping that they will be granted leave from Nigeria's pre-tournament training camp.
At present, Berti Vogts is expecting his players to meet up on 4th January in order to prepare themselves for the African Cup of Nations.
The former Scotland boss did reveal that he may be willing to allow his English-based players to play in the FA Cup third round on 5th January, but that he would then expect them to join the rest of the squad at their Malaga base.
With this in mind, Everton's 2-1 victory over West Ham on Wednesday night in the last eight of the Carling Cup now puts Yobo and Yakubu in a difficult situation.
The semi-finals are scheduled to be played on 8th or 9th January, but with the African Cup of Nations not beginning until 20th January, Yobo is hopeful that Vogts will relent and allow the duo to help Everton's bid for a first Wembley appearance since the 1995 FA Cup Final.
"We are going to try and work something out," the defender told the Liverpool Echo.
"I have got to stay focused on the games that we have coming up over Christmas and see where it leads me.
"I would like to delay it, but it's not up to me. It's up to the Nigerian FA and the manager. If the gaffer here tries and pushes, we will see what happens.
"The way we are playing, it is going to be very hard for me and Yak (Yakubu) to leave. We know that we have got to play for our country as well but we would like to sort something out if we can."
The Nigerian pair were in fine form as Everton disposed of West Ham at Upton Park, with Yobo a commanding presence at the back and Yakubu netting his seventh goal in his last seven games to send the Toffees through.
The win also stretched Everton's unbeaten run to 11 games, and Yobo believes that the side are now playing as well as they ever have done in the five years since he arrived at Goodison Park.
"It was a very tough game but we are all delighted," he said.
"Yak is in fine form and the team is playing well. He is a natural goalscorer and working really hard. I'm delighted for him.
"When the ball drops to Yak, you know he is going to score. But we have got other good forwards here who can also do the same. It's good from the team's point of view as it is giving us so much confidence.
"This run of form has been unbelievable. We have managed to cope with all the games recently, and it's the best I've known us play."