The holders will look to overturn a 1-0 deficit against Spurs at home on Thursday without the right-back, who was forced off the pitch in the 70th minute of Saturday's 2-0 Premier League win over Bournemouth.
Alexander-Arnold has played 31 games across all competitions this season, scoring two goals and registering seven assists.
"He left the pitch with a bit of a pain in his leg (at Bournemouth). He is already back on the pitch with the rehab coach so let's see how long it is going to take," Slot told reporters.
"We have to see if he can play Sunday (in the FA Cup fourth round), but he is not available tomorrow."
Academy product Conor Bradley is likely to replace the England international and Slot backed the 21-year-old to keep improving, having featured in 18 games in all competitions this season.
"He (Bradley) played against Spurs back (in the first leg) too. Every game and session there is something to learn and if not, it wasn't a good session from me," Slot said.
The manager said he was not going to undermine Spurs' depleted defence, even with Radu Dragusin likely out for the season due to an ACL injury and Cristian Romero, Destiny Udogie, and Micky van de Ven also sidelined.
"With all the injuries Spurs had last time, it would have been an advantage for us but we still lost against the ones who were fit," Slot added.
"I wonder if Micky van de Ven can play, (as) he has a big impact. It will be difficult but we will be better than the last time."