Right back Alexander-Arnold has not played since November 8, after having to come off in the second-half in the draw against Manchester City due to picking up a hamstring injury.
Keita, meanwhile, was forced off after 53 minutes during the win against Leicester nearly two weeks ago but Klopp said that both players could be available to him this weekend.
"There's a chance that Naby and Trent could be in the squad [for Sunday]," Klopp said at his pre-match press conference.
"I don't know yet, we will see. Trent and Naby will do their first steps in team training. We will see how it looks and how they respond.
"They haven't done a lot and we have to see how it develops."
Klopp also revealed that Oxlade-Chamberlain's fitness is improving, having not yet played for the Reds this season.
The 27-year-old sustained an injury to his knee during a tackle in pre-season, but Klopp is optimistic that the midfielder will be available soon.
"Oxlade [Chamberlain] looks really promising," Klopp added.
"He does the warm up with the team and we will develop that over the coming days. He's not far away."