The England international's return is a big boost for Liverpool ahead of a Champions League quarterfinal match at Benfica on Tuesday and a Premier League showdown with Manchester City the following Sunday.
But first is relegation-threatened Watford at Anfield.
"It will be tight for tomorrow but it's possible," Liverpool manager Jurgen Klopp said Friday.
The 23-year-old Alexander-Arnold was originally projected to miss at least two weeks, which had raised concerns about his availability for the April 10 game at City. Liverpool trails league-leader City by one point.
Alexander-Arnold's injury kept him out of the England squad for two friendlies but he was expected to rejoin full team training at Liverpool on Friday.
"Physically he should be fine. Now I have to make the decision about rhythm and these kinds of things," Klopp said.
The German coach also said top scorer Mohamed Salah will rebound from Egypt's failure to qualify for the World Cup. Egypt lost to Senegal on penalties Tuesday after Sadio Mané converted the winner.
Salah was targeted by laser pointers before missing his kick in the shootout.
"I'm obviously really happy for Sadio that he could make it and I'm obviously very disappointed and feel (for) Mo," Klopp said. "I don't think that the situation around with the penalty and the laser(s) was particularly cool. That's clear as well. So, I feel for him, but I'm happy for Sadio as well. That's football.
"Senegal is probably in the moment the best team in Africa," he added. "Egypt did really well. I'm not sure they can see it like this exactly but my point of view is they should."
Senegal's victory was similar to the African Cup of Nations final when Mané clinched a first major title for his country by also scoring the winning penalty in a shootout against the Egyptians.
