Matip has missed the last two league games after limping out of the draw against West Brom with a thigh strain.
Initial reports suggested around three weeks on the sidelines for the 29-year-old, meaning it would always be close as whether he could return against United.
Given Matip’s injury history, though, a later return would not have been a surprise.
Speaking on Friday lunchtime before training, Jurgen Klopp told reporters: “Joel is close.”
“[But] does it make sense now to throw him into a game with one or two sessions – which he didn’t do yet, but today and tomorrow he might be involved – and bring him in?
“I don’t know, we have to see. We have to decide it then. We have to look at him, how he trains and how he looks in training, these kinds of things.”
Matip has now taken part in Friday’s session and should no setback occur and he can train on Saturday too, then he is expected to be in the squad on Sunday.
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Having Matip able to start on Sunday would be a huge boost for Liverpool, meaning he could partner Fabinho in defence, allowing Jordan Henderson to line up in midfield alongside Thiago and Gini Wijnaldum.
Should Matip not be fit, Klopp would likely have to play Henderson at centre-back and bring Curtis Jones into midfield.
Liverpool are have also been boosted by a return to training for Kostas Tsimikas. The Greek left-back, who is yet to start a Premier League since his £12 million move last summer, had been sidelined with a knee injury suffered against FC Midtjylland in mid-December.