Klopp was left with just two fit senior central defenders - Virgil van Dijk and Joe Gomez - following injuries to Matip (knee) and Lovren (hamstring), while potential stand-in Fabinho (ankle) has been missing since the end of November.
He told Liverpool's website: "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."