Fabinho, 26, hasn't featured since he suffered an ankle injury in the first half of Liverpool's 1-1 home draw against Napoli on November 27, while Matip has been absent since October due to a knee problem.
"I wait really until they are on the pitch and somebody tells me they are allowed to do the full session.
"It looks like Joel will be in, it looks like Fabinho will be in maybe a day later, I'm not sure. Dejan, maybe he can be in as well. That means a lot and helps massively of course. But we will see how it looks. The week is very important.
"The game on Sunday against United, we all know what people expect from us from that game. It will be a big one as well, and we try to be ready for that."
Fabinho recently told Telefoot (h/t Liverpool's official website): "My ankle is getting better. I trained by myself this week. I was working with the ball again. I feel good and confident."
The Brazil international returned to individual training last week, and the Mirror's David Maddock wrote on Tuesday that he could face United in what would be his first league game since November 23.
Fox Sports presenter Keith Costigan lauded the efforts of Liverpool captain Jordan Henderson, who has retreated into a deeper-lying role of late to meet his manager's needs:
keith costigan @KeithCostigan
Think Klopp will handle that midfield 3 like he does the center back role alongside Van Dijk? Next man up and if you play well you keep your position. Interested to see if Fabinho comes straight back in. Was excellent earlier in season but Henderson has been excellent as DM
Klopp has rotated James Milner and Alex Oxlade-Chamberlain into midfield over recent weeks to help make up for Fabinho's absence, though each of those players have encountered fitness concerns themselves.
Adam Lallana has overcome his own injury woes to play his part, professing his desire to contribute however possible after Saturday's 1-0 win at Tottenham Hotspur, per the Liverpool Echo's Paul Gorst:
Joe Gomez has impressed as the centre-back partner of Virgil van Dijk during Matip's time outside the squad, with the 22-year-old playing the full games in each of Liverpool's last seven outings. That includes a 120-minute display in their 1-0 win over Flamengo in the 2019 FIFA Club World Cup final.
Van Dijk showed his appreciation for Matip's new look ahead of his team-mate's possible first-team return:
Liverpool will move 30 points above United—currently fifth—if the Anfield hosts win in Week 23, though the Red Devils have managed draws in their last two meetings (both at Old Trafford).
Xherdan Shaqiri scored twice off the bench when Liverpool won 3-1 the last time these teams met at Anfield (Dec. 2018), and Klopp will hope he can rely on his recovered reserves to help prevail on Merseyside.