Chelsea have 11 first-team players out, including winger Raheem Sterling and goalkeeper Robert Sanchez who are ill.
"(Enzo and Disasi) have different types of issues. We don't believe they're big issues but we'll see if they can be available," Pochettino told reporters on Friday, adding the duo had not trained since Sunday's 2-2 draw at Sheffield United.
"(Full-back Ben Chilwell) is training, partial training and see if he can be involved in the squad on Monday. It's good news, but he hasn't played too much this season," he added.
Chelsea's injury crisis has been one of the main reasons for their lack of consistency this season, the Argentine said.
"It should be fair to have a fit squad to prove that we are a good squad and we can compete for big things. At the moment it's not fair to the players," he said.
"It's really, really tough when you don't have a squad fit enough to increase competition between them."
Pochettino said he was considering bringing some academy players into the squad against 16th-placed Everton.
"Chelsea have one of the best academies, not only in the league, but in the world... they are going to have the possibility to be involved in the squad on Monday, a few of the players," he said.
Chelsea, ninth with 44 points, are five points off the top six as they look to secure a place in European competition.
"We are changing but we are still not in the level to be consistent enough. We were working a lot this week and hope little by little we will change," Pochettino added.
