Alexander-Arnold has been absent since Liverpool’s 1-1 draw with Manchester City last month while Keita left during their 3-0 win over Leicester City with a similar problem.
However, Klopp revealed the pair may play against Wolves at Anfield on Sunday.
“Trent and Naby will do the first steps in training today,” Klopp told a media conference on Friday.
“There’s a chance that Naby and Trent could be in the squad, but if they can play 90 minutes, I don’t know. Apart from Naby and Trent, nobody else is coming back.” Jürgen added.
Liverpool will play a game at Anfield in front of supporters for the first time since March, with 2,000 fans allowed to assist after coronavirus restrictions were eased.
Klopp encouraged his players to produce a performance worthy to welcome their fans’ return to the Anfield.
“I hope it will be a great experience for all of us,” said the German.
He continued “Now we have a few fans back, especially nice for the people. Very important for the clubs because it gives us the chance to show that we can deal with it and maybe soon we can bring in more people.”