Alli, who played the final 20 minutes of Thursday's defeat to Sheffield United, has been plagued by hamstring problems, twice suffering strains last season and missing two matches in August at the start of this term.
Mourinho revealed Alli's latest issue is troubling the club's medical department given his history but says he expects the midfielder to feature against the Toffees.
"[There was] something today in training with Dele Alli," Mourinho told a press conference on Saturday.
"When I say 'something', it's because I don't think it's big and I don't really know what it is. The bad thing about a press conference 48 hours before the game is there's still a session tomorrow, so you will not know what I know, if he is available or not.
"[It's his] hamstring, which is something which he had problems with in the past, in previous seasons, even the beginning of this season, and it's always something that makes the medical department think. We all think it's nothing important and if you ask me in this moment I would say he'd be available. But I don't know."
Mourinho will definitely be without young defenders Japhet Tanganga and Juan Foyth, and he revealed the former is unlikely to play again this season after a stress fracture to his back.
"Japhet Tanganga we believe training with the team next week," Mourinho said. "Could he play again this season? Too long without playing and an important injury, so I don't think so. Two weeks to work and be available for the last match, maybe. But to play safe, young guy with a very important injury, probably the best thing for him is to be back for next season."
Mourinho's faces a challenge to lift his players for the visit of Carlo Ancelotti's side after a chastening 3-1 defeat in Sheffield all but ended Spurs' Champions League hopes.
The visitors crumbled at Bramall Lane after Harry Kane's equaliser was ruled out by VAR Michael Oliver for a Lucas Moura handball but Mourinho insisted the decision was not the sole reason for their defeat, claiming his side's lack of desire left him feeling disturbed.
"I thought that by a desire point of view, they put more than us," he said. "That's something that disturbs me. It's something that I feel, that's my way of being.
"It's something that destroys me a little bit on the inside because I think the last thing in football is when you have the feeling you could, you should do more.
"It's not a problem for me to cope with mistakes and defeats. It's a problem when my feeling was we could do much more. In this moment I'm not happy but experience and I know that we have another match after tomorrow. We have six matches to play and before the holiday period and we have to fight for every point."
Mourinho also criticised his players mentalities immediately after the defeat in Yorkshire – which left Spurs seven points behind Manchester United and Wolves – and claimed they had to learn to respond to setbacks.
Asked what it would take to change their mindsets, he said: "Time. Only time. One of the most difficult things in football is exactly that, to change mentalities. It's to change state of mind. It's to change the team's soul. It's one of the most difficult things in football. Sometimes you have incredible luck to have a majority of players adapted to these needs and some other times you have incredible players but the psychological profile is different or was built in a different direction.
"So only time can do it. You have a recent example of the new champions and you know what the process to build the team is."