The England midfielder was on the receiving end of a reckless tackle from Raheem Sterling in Spurs' 2-0 victory over Man City on Sunday.
Referee Mike Dean showed a yellow card to Sterling, who Mourinho thought was fortunate to stay on the pitch following a VAR check for a possible red card.
Despite being substituted with 20 minutes remaining, Mourinho is hopeful Alli will be fit to face Southampton in Wednesday's FA Cup fourth round replay, which is LIVE on talkSPORT.
He said: "It's not as bad (as we thought), so there is a chance.
"There is a chance of him playing tomorrow, so wait and see, but there is a chance.
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“It is just a question of being a little bit lucky or unlucky. You need a little bit of luck.
“Dele Alli was very lucky. Did Sterling want to injure him? I don’t think so, I don’t believe that he wanted to.
“So respect to Sterling, I have no problem at all. But the intention does not count. What counts is the action. It is a red card.”
Mourinho received more promising injury news with Ben Davies' return to full training after recovering from an ankle issue.
The left-back, who has been sidelined since November, is set to be in contention for Tottenham's trip to Aston Villa on February 16.
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Mourinho said: "He’s training with us since Monday.
"Of course, after (Wednesday) the boys are going to have some time (off) but not him, he has to stay and work.
“So when we start the week of Aston Villa he will be training with us fully, so if everything goes well he will be good for the Villa game.”
Tottenham boss Jose Mourinho has confirmed Dele Alli's ankle injury is 'not as bad' as first feared.