Matip suffered a calf injury during Liverpool's 3-2 loss at Arsenal over the weekend, while Alexander-Arnold sustained an ankle problem in the same match.
Both players are understood to have been ruled out of this week's Champions League trip to Rangers as well as the showdown Premier League champions Manchester City at Anfield this weekend.
Losing the two defenders is another setback for Liverpool boss Klopp after Luis Diaz recently learned he will be out until after the World Cup with a knee injury suffered in the Arsenal loss.
The Colombia forward left the Emirates Stadium on crutches and with his knee in a brace.
Ibrahima Konate made his first appearance of the season after an injury of his own when he replaced Matip as a substitute against Arsenal and the French centre-back is set to start alongside Virgil van Dijk at Rangers.
Central defender Joe Gomez will likely fill in at right-back during Alexander-Arnold's absence.
Veteran midfielder James Milner has also featured at right-back in the past, while Calvin Ramsay was included in the match-day squad for the first time since arriving from Aberdeen in the summer transfer window when Liverpool beat Rangers last week.
Klopp has been battling with injuries from the beginning of a troubled season, with Liverpool's fitness woes playing a role in their worst start for 10 years.
The club are languishing in 10th place in the Premier League, 14 points off the top after winning two of their first eight games.
Brazilian midfielder Arthur Melo, who has played just 13 minutes since his loan move from Juventus, faces months on the sidelines after picking up an injury in training.
Fellow midfielders Alex Oxlade-Chamberlain and Naby Keita are seemingly also out of action.
Klopp hopes to have Curtis Jones available to face Rangers, while Scotland left-back Andy Robertson could return to the squad this week.
