The Guinean has been sidelined since suffering a hip injury in training ahead of the UEFA Super Cup in August, having already spent much of the previous three months out with an adductor problem.
It has been a difficult spell for Keita at Liverpool so far, but Klopp has kept his faith in his No. 8, with the hope being he can settle and consistently show the form that prompted his £52.75 million move from RB Leipzig.
Instead, he is pencilled in for his comeback at Stadium MK in midweek, with this providing a more comfortable fixture to ease the 24-year-old back in.
“He is close but the matchday squad is not yet the target. It is a few sessions training with the team,” Klopp told reporters.
“We’d only put him in [at Chelsea] if we didn’t have enough players but I hope we will have enough players for the matchday squad.
“Wednesday is the target I will say and then we will see.”
That is, of course, no guarantee Keita will start against MK Dons, and it is perhaps unlikely given he is yet to play since his 23-minute cameo in the Community Shield on August 4.
It could be that the manager turns to some of his younger talents, too, though the under-21s take on Fleetwood Town in the EFL Trophy on the same night.