Matip was one of three players to pick up an injury against Everton on Saturday.
Midfielder Fabinho is expected to partner Joe Gomez at the back.
Midfielder Thiago also misses out after injuring his knee and goalkeeper Alisson remains on the sidelines.
Van Dijk suffered an anterior cruciate ligament injury in the Merseyside derby after a challenge by Everton’s Jordan Pickford.
Returning to action after knee surgery can take many months and Liverpool are refusing to specify how long Van Dijk will be out for until after his operation.
“We know our vice-captain and best centre-back in the world is not playing for us for a long time,” Klopp said.
“We will try to find solutions, but I have no idea how they will look.”
Ajax manager Erik Ten Hag says Van Dijk’s absence won’t change how his side approach the game.
“At the end of the day it is about who is still playing. It’s not going to be a different Liverpool, they always play the same,” said the Dutchman.
“The quality of Man A can switch to Man B, the whole team won’t change because Virgil Van Dijk isn’t present.
“They are currently the best team in the world, if you win the Champions League and Premier League within two years you are a strong contender for the Champions League title.”
Ajax’s home struggles – the stats
- Ajax and Liverpool will meet for the first time since the 1966-67 European Cup, where the Dutch side eliminated the Reds with a 7-3 aggregate victory in the Last 16.
- Since losing 5-1 against Ajax in December 1966, Liverpool have gone unbeaten in their 13 games against Dutch opponents in European competition (W8 D5).
- Ajax have only won one of their previous six games against English opponents in European competition (D2 L3), going winless in the most recent three since a 1-0 victory against Spurs in the Champions League semi-final first leg in 2018-19.
- Ajax have won just one of their previous seven home games in the Champions League (D2 L4), with two of the last three defeats in this run coming against English opponents – 2-3 v Spurs in May 2019 and 0-1 v Chelsea in October 2019.
- Liverpool have lost their last two games in the Champions League (both against Atletico Madrid last season), while they have not suffered three consecutive defeats in the competition since October-November 2014, under Brendan Rodgers.
- Ajax’s Dusan Tadic has had a direct hand in 13 goals in 18 appearances in the Champions League (six goals and seven assists); the most of any player for the Dutch side since the start of the 2018-19 campaign.
- Roberto Firmino has been directly involved in 26 goals in 33 Champions League games for Liverpool (15 goals and 11 assists) – since his debut in the competition in 2017-18, the only other player to have scored 10+ goals and made 10+ assists in this period is Kylian Mbappe (13 goals, 13 assists).
- Should he appear in this game, Klaas Jan Huntelaar (37y 71d) would become just the second player to feature for Ajax in the Champions League at the age of 37, following Danny Blind back in 1998.
- Since making his Champions League debut for Liverpool in September 2017, Mohamed Salah has netted 19 goals in the competition for the Reds – the most of any player for an English club in this period.