Matip suffered a shoulder injury in a collision during the closing stages of Tuesday's win at Anfield before Alexander-Arnold limped off in stoppage-time and had to be replaced by Dejan Lovren.
Several media reports now claim Matip has now been taken to hospital for scans on the injury, though Reds boss Jurgen Klopp couldn’t confirm those reports when asked by the media after the game.
He did, however, confirm that England full-back Alexander-Arnold is to be assessed after picking up a foot problem.
“I’m not sure,” said Klopp. “Nobody told me anything about [Joel’s] shoulder, so hopefully that’s a good sign.”
“Trent got a knock on his foot, we are not sure about what exactly it is. It is painful."
James Milner was also forced off the field, but Klopp has revealed the former Manchester City man was only suffering from cramp.
“Millie [Milner] had cramps – I hope it was only cramp. That was it, I don’t know anything else," added the Liverpool boss.
The Reds finished level on points with their Italian opponents but progressed at their expense on goals scored.
The Merseysiders are already without Joe Gomez, who has been sidelined for around six weeks with a broken leg suffered against Burnley last week.
If Matip is ruled out for a significant period of time it would mean Lovren and Virgil van Dijk would be Liverpool’s only two fit centre-backs heading into the busy Christmas period.
The Reds are currently one point clear at the top of the Premier League after their win over Bournemouth last weekend combined with City’s defeat at Chelsea.
Champions City host Liverpool’s Merseyside rivals Everton this Saturday lunchtime before United head to Anfield 24 hours later.