The 24-year-old's future at Spurs is uncertain after he was left out of their last two matchday squads against Southampton and Lokomotiv Plovdiv.
A number of clubs, including Paris Saint-Germain, are interested in signing the England international in this transfer window but Mourinho is confident Alli will stay in north London.
Asked if Alli will be at Spurs by the end of the transfer window, Mourinho told Sky Sports News: "I believe [he will]. I can even say that I'm convinced that he will be."
Alli has been included in Spurs' squad for their trip to Macedonia to face Shkendija on Thursday in the third round of Europa League qualifying.
Mourinho, who is yet to decide whether or not Alli will start against Shkendija, says the midfielder lacks consistency and has challenged Alli to prove himself.
Speaking at his pre-match news conference Mourinho said: "We all know since Dele arrived from MK Dons he had ups and downs, he had fabulous periods and he also had other periods where he disappeared from top-level performances. And with me it's no different than before.
"He's had moments where he was so good, but he also had moments where he was not so good.
"I think this lack of consistency, it's normal that when you are in great form you play because you deserve it and your production is big for the team, but when you are not in a good moment you don't play - and it's as simple as that.
"The players have to prove on the pitch with their performances; they have to prove how good they are in that specific moment.
"Tomorrow (Thursday) he is selected but there is no decision yet about starting or being on the bench, but when he's selected he has a chance to play.
"If he's on the pitch one minute or 90 minutes he has to show us - it's that simple.
"There's no problem at all to have him, and, like every other player, performances are important."
Mourinho, who called Alli a "lazy" trainer in the recent All or Nothingdocumentary, believes he cannot be blamed for Alli's recent poor form.
The Portuguese said: "There is tendency now that when a player performs or doesn't perform to give responsibilities on coaches because they gave him the right stick, but I always feel that 99 per cent of the responsibility is the player.
"I have one per cent; me and my staff and the people that work with the players everyday - we have one per cent of that responsibility. It 99 per cent belongs to them."
Mourinho hopes Bale can extend Tottenham stay
Mourinho is also hopeful Gareth Bale can stay at Tottenham beyond his season-long loan deal.
The Wales forward has returned to Spurs on loan, seven years after leaving the north London club for Real Madrid in an £86m transfer.
Asked if Bale will stay at the club for more than a year, Mourinho told Sky Sports News: "If everybody's happy, it would be perfect.
"I didn't speak with Zinedine (Zidane) but I believe that Zinedine is happy that he left, we are happy that he is here and Gareth of course is happy to be here, so hopefully at the end of the season we are all happy and he can stay with us."
Mourinho also admitted he wanted to sign Bale while in charge at Real Madrid and Manchester United, but he has warned the 31-year-old he will have to earn his place in the Spurs team when he becomes fully fit.
"He knows that I wanted him at Real Madrid but in that season it wasn't possible," Mourinho said. "He also knows that there was a little bit of an open window to try to have him at Manchester United.
"He knows that he's a player that I like very, very much so he has this positive feeling with me.
"But he knows with me it's the best one who plays; he will not play because he's Gareth Bale, he will play because he will show that he's better."
Source: Sky Sports