The knock forced him off during Liverpool’s win over Bournemouth in the Premier League over the weekend.
The vice-captain pulled up in the second half and was replaced by Conor Bradley as a precaution.
Arne Slot confirmed after the match that Alexander-Arnold requested to come off to avoid making the problem worse.
He stated post-game: “The situation is he said to me that you have to take me off and he sat on the floor and we took him off.
"He felt something, I can’t tell you exactly what it was and how bad it is as we are (talking now) only just after the game.
“But it’s never a good sign if a player is asking for a substitution. It’s not a fact but I would be surprised if he plays on Thursday. Let’s hope he is back with us as soon as possible.”