Fabinho took part in first-team training at Melwood on Wednesday for the first time since his ankle injury, but three others were absent.
The Brazilian has been sidelined since suffering ligament damage in the 1-1 draw with Napoli in the Champions League in November, missing the last 12 games.
His absence has not been felt as heavily as expected, with Jordan Henderson shining in the No. 6 role, but a return to action will be hugely appreciated at Anfield.
Klopp said Dejan Lovren would “maybe” be in contention for the United game, but he was not among the squad warming up in front of the cameras at Melwood.
The remainder of the squad are fit as preparations continue, with Ki-Jana Hoever, Neco Williams, Pedro Chirivella, Curtis Jones and Harvey Elliott increasing the numbers after their roles in the under-23s’ 5-0 win over Southampton on Monday.
It is unclear how Klopp will set his side up against United, who are the only side to take points from Liverpool in the league so far this season.
Klopp will hold his pre-match press conference on Friday, when he is likely to provide a more accurate assessment of his squad’s fitness.
Liverpool Squad in Training on Wednesday
Defenders: Van Dijk, Gomez, Matip, Alexander-Arnold, Robertson, Williams, Hoever
Midfielders: Henderson, Wijnaldum, Fabinho, Oxlade-Chamberlain, Lallana, Jones, Chirivella
Forwards: Salah, Mane, Firmino, Origi, Minamino, Elliott
* Goalkeepers trained separately.