The duo underwent scans and trained with the first team on Thursday but Pulis said he would wait a little longer to decide which of the two will be in goal against Southampton.
"They will do a little bit more (training) today. We hope that one of them will be fit enough to stand but we don't know which one," Pulis told a news conference on Friday.
"It is going to be a big 48 hours for us as a team and club in respect to the two goalkeepers," added Pulis, whose only other option is 21-year-old Alex Palmer, who has not made an appearance for the club yet.
Striker Hal Robson-Kanu (muscle strain), winger Oliver Burke (hamstring) and midfielder James Morrison (calf strain) will miss the Southampton clash but are in line for a return when league leaders Manchester City visit West Brom next week.
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West Brom, 10th in the table with 10 points, have conceded nine goals this season - two more than they have scored - and Pulis said that the team had to be more sharp up front and tighter at the back as the season rolls on.
"As a team we need to score more goals," said Pulis. "We've looked back on the goals that we've conceded. It's been more individual errors than anything else. That happens sometimes."
Southampton, who were held to a 2-2 home draw by Newcastle United in their last game, have a similar goal difference and are one spot below West Brom in the table with nine points from eight games.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Pritha Sarkar)
