Albion head coach Graham Potter confirmed the match against Carlo Ancelotti's men will likely arrive too soon for two of his players.
Davy Propper has yet to feature in the Premier League this season due to an Achilles problem while Alireza Jahanbakhsh injured his hamstring during Wednesday's 3-0 Carabao Cup loss to Manchester United.
Propper, 29, was making progress from his injury and played in the League Cup matches against Portsmouth and Preston but missed last night's defeat to United as the problem flared up once more.
The midfielder is also expected to sit out of Holland's next three matches of the upcoming international break against Mexico, Bosnia and Italy.
"Davy is still (injured) and the Everton game might arrive too soon. But we are hopeful for him for the other side of the international break," said Potter
The injury to Jahanbakhsh is also a set back for club and player. The Iranian international has been excellent for Brighton in the League Cup this season and was pushing hard for a starting role in Potter's Premier League team.
He hobbled off in midweek against United on 50 minutes and was replaced by Neal Maupay.
"Ali probably will not be able to recover in time," said Potter. "He is going in for another look (at the hamstring) this afternoon and we will have some more information there. But at the moment it looks like he will also miss out."
Florin Andone (knee) and Jose Izquierdo (knee) are long term absentees while reserve goalkeeper Chris Walton remains sidelined having injured his ankle in pre-season against Chelsea.
On the plus side midfielder Yves Bissouma is available for selection at Goodison Park having served his three match suspension following a red card at Newcastle.
Potter anticipates a tough encounter against an Everton who have won their first three matches and in Dominic Calvert-Lewin they have a striker at the top of his game.
Calvert-Lewin earned his first England call-up by Gareth Southgate today after scoring eight goals in five appearances in all competitions so far this season, including two hat-tricks.
"He has taken his game up to another level," said Potter. "Goals and confidence helps but he is a striker that has got everything. He deserves his call-up and hopefully he's celebrating a lot and doesn't play so well on Saturday.
"Everton have been really impressive. They have really invested and have a very high quality manager. They have some really good players and they have a good balance.
"He (Ancelotti) has looked at the squad made adjustments and improved them. He is someone I look up to a lot and respect because of the career he has had and the job he is currently doing."