Alisson missed Liverpool's 2-1 defeat to Brighton & Hove Albion on Saturday and will not link up with the Brazil squad for their forthcoming matches.
Ekitike, meanwhile, was forced off after eight minutes of the Premier League contest at Amex Stadium.
In his post-match press conference, Slot said: "Alisson will definitely be out during the international break and let's see afterwards.
"Hugo, I think he could play tomorrow if he needed to. It was a dead leg, as you call it here I think.
"Brighton did what we expected. If you face a team that has only had 62 hours of rest and the first thing you do is make it an intense game, play the first duels, play tough duels – nothing wrong with the duels, by the way – but unfortunately it was a collision and that led to Hugo going out."
