The Egypt captain, the league's second-highest scorer this season with 14 goals, had picked up a hamstring injury during the Africa Cup of Nations in January.
Alexander-Arnold, meanwhile, suffered a recurrence of a knee injury during Liverpool's 3-1 home win against Burnley last weekend. He is set to miss the League Cup final against Chelsea later this month.
"Mo is back in full training, so that brings him back into contention," Klopp told reporters ahead of his side's trip to West London.
"Ibou (Ibrahima Konate) is not suspended anymore, Joey (Joe Gomez) is fit again, Conor (Bradley) is back, Ali (Alisson Becker) is back, so that's all positive. Thiago (Alcantara), no. And Trent not (available)."
The German coach dismissed suggestions that Alexander-Arnold was rushed back after his injury.
"I got the news that there was a discussion we might have 'forced' Trent back because of two setbacks. Nobody wants that and nobody is doing that," Klopp said.
"The boys were in the moment when they played. They were fit. But the situation told us differently because it happened again. Very unlucky and unfortunate, but it can happen.
"We have to bring the boys back as soon possible but never before they are ready."
Klopp was also asked if midfielder Dominik Szoboszlai, who remains out after aggravating a hamstring injury, will be fit in time for the League Cup final on February 25th.
"It's a super intense period. People think now about the final, absolutely, but before that we have Brentford and Luton (Town), I'm not thinking a second about the final yet," he said.
"With Dom, it will be around that time (the final) we will see how that exactly how works. With Trent maybe a week or two longer so it's not great. I would say not sure if Dom has a chance for the final, but maybe. Trent will be after."
Klopp was full of praise for their next opponents Brentford.
"It is super tricky there... they are well organised, set-pieces, cheeky, rhythm breaks and they are good at set-pieces which they want. That's how it is," he said.
"They are more than just set-pieces. They are compact. They are well coached and the atmosphere the stadium creates is really good.
"We have to be at our best to win at Brentford. It's a smart coached team."
