Matip was hurt in a collision during the last stages of the game and according to the Standard, the defender had to be taken to hospital to undergo tests on a possible shoulder injury.
Meanwhile, Alexander-Arnold was forced off in the 90th minute and replaced by Dejan Lovren after he suffered a foot injury.
According to the Echo, the youngster is also undergoing scans on the injury and the concern will be that he will be sidelined for a run of games.
James Milner also went off with cramp in the 85th minute, although Klopp admitted he was unsure if it was "only cramp."
Speaking after the match, Klopp played down the injury to Matip, saying of the trio: “I'm not sure. 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.
“Millie had cramps – I hope it was only cramp. That was it, I don't know anything else.”
With Joe Gomez's absence, the Reds defence can't afford to be on the receiving end of any further injuries.
If the Reds are indeed without Joel Matip and Alexander-Arnold at the back, it leaves just Lovren, Virgil van Dijk, Andy Robertson and Alberto Moreno as the only fit recognised defenders in the squad.
The manager may have to look to Fabinho in the right-back spot against Manchester United if Alexander-Arnold is ruled out, although Milner is another option if he has recovered.