The England centre-back sustained a knee injury in Tuesday's Leuague Cup victory at Reading but a late decision will be made on whether he is ready to play at the Hawthorns.
His withdrawal just after the half-time break at the Madejski was the first time this season he has not finished a match and his absence would be a blow for Martinez.
"We have been pleased with John's reaction to treatment in the last couple of days but I still think the next 48 hours are very important," said the Toffees boss.
"I wouldn't say he is not going to be in the squad but it is too early to make a final decision.
Leighton Baines is nearing a return after injury
"It will be touch-and-go for the West Brom game."
Martinez has been boosted by the fitness news on two other England internationals at the club.
Midfielder Tom Cleverley is ahead of schedule in his recovery from an ankle ligament injury and could be available to face former side Manchester United at Goodison Park on October 17 - when left-back Leighton Baines may also return from an ankle problem.
"Tom avoided surgery. He wants to play against Manchester United," Martinez told the Liverpool Echo.
"That is a realistic target and is three weeks earlier than we thought. Leighton is the same."
