The centre-back has missed three matches with a hamstring injury and if he is not considered fit enough John Stones will continue to deputise.
Midfielder Steven Pienaar, who missed last week's win over Cardiff with a knee cartilage problem, is expected to be out for a further two to three weeks.
The 35-year-old former club captain was put in interim charge when Michael Laudrup was sacked in early February despite having no previous experience.
In his first month in charge he had to balance the demands of the FA Cup, Europa League and Barclays Premier League.
Despite exit from both cup competitions, their league form has not improved and Monk has won just once - his first game against south Wales rivals Cardiff - as the side have picked up five points from as many matches to leave them perilously close to the relegation zone.
Martinez admits he has a soft spot for his former club and, ahead of their third meeting this season, has backed Monk to keep them in the top flight.
"I have been very impressed with Garry Monk and it would be a big mistake to try to assess his time just by the results," said the Spaniard.
"Some of the performances have been impressive, especially the two games against Napoli in the Europa League where he brought a mature performance from the players.
"Even the game against Liverpool (losing 4-3 at Anfield) and games at home to Crystal Palace (1-1) and West Brom (a 2-1 defeat) have been very small margins and that is why they are where they are in the league.
"I don't think there is a big difference or something huge lacking.
"I have been very impressed with the way he has handled the demands of a short period of time with so many games.
"Everyone has had a good reaction and I know it will be a really tough game for us on Saturday."
Everton are currently sixth, occupying the final Europa League spot, but Martinez knows they will have to win the majority of their remaining 10 matches to keep their European dream alive.
Manchester United are three points behind, having played a match more, but fifth-placed Tottenham could well be caught as they are only two ahead having played two games more.
"Thirty points is a huge amount. We are playing for 15 points at home, which is something we welcome as our football at Goodison has been full of confidence and good play," added Martinez.
"Our points average at home has been exceptional and we need to carry on with that but in the same manner you need to be able to go away from home and get competitive performances."
Striker Michu is set to continue on the comeback trail for Swansea.
Michu returned off the bench after three months out with an ankle injury when Swansea lost at home to West Brom last weekend.
Jonjo Shelvey, who has had hamstring trouble, looks poised to feature at Goodison Park, along with Nathan Dyer, who also missed the Albion clash as he rested a heel injury.
Monk is "totally confident" his Swansea team will collect enough points to finish clear of the relegation zone.
The loss against the Baggies means Swansea go into the clash at Goodison Park just four points above Sunderland, who lie 18th.
They have not claimed a league win since beating Cardiff, and the West Brom result certainly provided a piercing wake-up call if one was required.
"The first thing I said to the players (last Saturday) was 'you are now going to learn exactly what it's like to fight'," head coach Monk said.
"You could see West Brom's attitude in the second half. They upped the spirit and intensity, and at that point we couldn't match it.
"The positive was that we saw a team fighting for their lives. Some players will not have experienced it before, but it is at times like this you see who is a boy and who is a man.
"The reaction in training this week has been good. All the players have been pushing each other.
"But the ultimate point is you've got to turn those performances into results. If I am not happy I will tell them, but they weren't happy themselves."
- Sports & Recreation
- Europa League
- Garry Monk
- Barclays Premier League