Gibson suffered a knee injury in the pre-season friendly against Real Betis last month while Alcaraz is recovering from a hernia operation, but otherwise Martinez has no new injury concerns.
Speaking ahead of the Sky Live clash, Martinez said: "Darron and Antolin are in training with the first team.
"Now it is a case of getting the match fitness. That could take a couple of weeks, depending on how they react.
"Darron and Antolin won't be fit for the weekend but they are not going to be too far away. For Darron, in a couple of weeks, he'll be getting really close."
Martinez will consider handing debuts to new signings James McCarthy and Gareth Barry for Chelsea's visit, but Romelu Lukaku will not be involved against his parent club.
"It's been a real joy to see Gareth Barry around, with his daily standards," Martinez added.
"James McCarthy hasn't been able to train with the group yet, Romelu has been with us a couple of days. It is always great to have new faces being integrated into the group.
"I don't think it has been a difficult time for any of those players. It has been a good welcoming period. We can't wait to get the full squad working together.
"On paper, it seems everyone is more or less fine. A couple have niggles - Seamus Coleman and James McCarthy after their game with the Republic of Ireland - but apart from those two, everyone seems to be fully fit."
Martinez expects a tough examination from Chelsea but hopes that his team will rise to the challenge this Saturday evening - and record their first win of the season.
"As you know, Goodison has been a place to play our football and we want that to continue and we want it to be a difficult place for any team to come," he said.
"It will take a lot to beat Chelsea this season. Looking already, they are unbeaten - they've already visited Old Trafford. I think you're looking at experience and the amount of talent that they have. You'll do really well to beat Chelsea this season."
You can follow Everton v Chelsea on Sky Sports 1 from 17.00 on 14 September