The former Wigan manager takes charge at his new club's home for the first time after a 2-2 opening-day draw with Norwich City, while Nicolas Anelka misses out for Steve Clarke
The Spaniard saw his team take a well-earned point away to Norwich City in the opening game of the season, denied only by a superb header from Ricky van Wolfswinkel, who levelled the game at 2-2.
Steve Clarke will have to revitalise his charges as they fell to a 1-0 defeat at home to Southampton on Saturday courtesy of a 90th-minute penalty from Rickie Lambert.
Everton lead the head-to-head meetings in the league between the two sides, with 60 wins to West Brom's 54, but they took a win apiece in the Premier League last season.
West Brom have lost on their last two league visits to Goodison Park, their last success at the ground a 4-1 romp in November 2010.
Sylvain Distin is a doubt for the hosts after picking up a knock in the draw with Norwich but full-back Tony Hibbert could feature after returning to training on Monday. However, summer signing Antolin Alcaraz is definitely ruled out with a hamstring injury picked up in pre-season.
|GOAL PREDICTS THE PL
|16/1||Everton and West Brom are 16/1 with Bet365 to draw 2-2
"Distin is the one we're a little bit concerned about," Martinez told the club's official website, "but, knowing Sylvain, you can never say that he's not going to be available at the weekend.
"Darron Gibson is progressing really, really well. It's one of those injuries where you need to be very, very careful you don't come back too early. He's still 50-50 for the weekend but I don't expect it to be much longer than that."
West Brom head into the fixture without close-season signing Nicolas Anelka, who has been excused from the squad on compassionate grounds. Zoltan Gera and George Thorne (both knee) remain long-term absentees.
Clarke's side will look for a quick response to their opening-day defeat and midfielder James Morrison is keen to make amends.
"For us, we need to get last Saturday out of the system, because it wasn't great," he told the club's official website. "It's a new era for [Everton], they have a new manager who will probably bring a new style to them.
"It's always hard to go to Goodison Park; we haven't had a great record there in the last few years apart from the 4-1 win. It's a hostile crowd, they're always on top of you, and, if you don't start right, you find yourself in for a tough afternoon."