The Brazil international sat out the weekend's 3-0 Premier League win over Bournemouth due to a muscular injury, which he had sustained prior to the Champions League win over AC Milan.
Alisson made it through that 3-1 success at San Siro last Tuesday, but he exacerbated the problem against the Rossoneri, allowing Caoimhin Kelleher to make his first start of the season versus the Cherries.
Kelleher was always expected to get the nod in goal for the EFL Cup, and speaking to the media in his pre-game press conference, Slot confirmed that the Irishman would continue in goal as Alisson looks ahead to Wolverhampton Wanderers at the weekend.
However, the Dutchman conceded that it would be "tight" for the South American to return for Liverpool's next Premier League game, saying: "It's sure that Caoimh will be in goal tomorrow.
"Alisson is getting there but I think this game is coming just a bit too early and we are looking at the weekend against Wolves, but it's going to be tight so let's see if he manages to be there."
Slot 'not at all surprised' by Kelleher's Bournemouth display
With Alisson sidelined at the weekend, Kelleher excelled in between the posts, making a crucial near-post save from Luis Sinisterra before a heroic goal-line clearance to prevent Trent Alexander-Arnold turning the ball into his own net.
The 25-year-old's standout display came after he vented his frustrations at not being able to leave Liverpool over the summer, but Slot talked up the importance of having multiple "quality" players in every position.
"I wasn't surprised at all with his performance [against Bournemouth] because he was very good in pre-season already and he was very good with his national team as well," Slot added.
"It's a good thing for us that we have two quality players, and we forget the third one in this position because in almost every position we have two but in goalkeepers we have got three or four and our third one is also a really good goalkeeper. So it's a good thing for us.
"Like you saw, we need to have a strong squad because you can pick up injuries or whatever can happen. So, it was good to see and pleasing to see that he kept a clean sheet - not in a way that he had nothing to do, he had to act a few times and he acted really well."
Could Federico Chiesa start against West Ham?
Alisson is one of two Liverpool players sidelined for Wednesday's game alongside foot fracture victim Harvey Elliott, and Slot will be expected to make a raft of changes with almost a fully-fit squad at his disposal.
Summer signing Federico Chiesa - who is yet to start for his new club since his cut-price move from Juventus - is among the players pushing for promotion to the first XI, and Slot has confirmed that the Italian is in contention for his full debut.
However, the Liverpool boss cannot see Chiesa lasting the full game due to his lack of preparation, adding: "I don't think he's able to play 90 minutes, he only played 25 now as a maximum in the last three, four, five months.
"I don't think he played any friendlies at Juve as well. But he is able to start, in our opinion, and if he will, let's see. There are many options we have.
"But he is able to start, in our opinion, but I don't think he is able to play 90 at the level we are playing tomorrow against a strong West Ham team."
Liverpool crushed West Ham 5-1 in the quarter-finals of the 2023-24 EFL Cup en route to their record-extending 10th title in the competition, and Jurgen Klopp's final trophy in his distinguished Anfield career.