The right-back sustained a knee injury before the international break and when asked for an update, Slot said that there is no return date.
He said: "His situation is that unfortunately he is injured. He is fully focused for his recovery and for us we are trying to help him to be back as early as he can."
Alexander-Arnold has been a key player for the Merseyside giants. He has managed 10 goal contributions for the Reds in the current season.
It remains to be seen whether he will return before the campaign ends. It appears unlikely that he will continue with the club beyond June.
His current deal expires on June 30 and reports claim that Real Madrid are discussing a pre-contract with the right-back over a free transfer.
It is anticipated that an agreement will be reached this month.