Knee surgery kept Van Dijk sidelined for most of last season and this year's European Championship.
The 30-year-old Dutch international central defender's new deal is reported to tie him to the club till 2025.
Van Dijk had surgery on a knee injury and Klopp had previously said he thought the European tournament would likely come too early for the centre back.
Liverpool are unlikely to sign a central defender in January as cover amid an injury crisis at the Premier League club.
Klopp has said he hopes the club’s young centre backs can step up in the absence of injured regulars as the Premier League champions cope with an injury crisis.
Fabinho has been filling in for Van Dijk in the centre of defence since the Dutchman suffered a serious knee injury.
Liverpool have the quality in their squad to deal with the absence through injury of influential centre back Virgil van Dijk, said skipper Jordan Henderson.
Ancelotti said Pickford’s challenge on Virgil van Dijk was mistimed rather than malicious and that reaction to the incident was over the top.
Klopp is confident defender Virgil van Dijk will come back stronger as the Dutchman undergoes knee surgery and faces a battle to play again this season.
The champions must look to sign a replacement in the January transfer window, former defender Jamie Carragher said.
Virgil Van Dijk fears Liverpool will be forced to celebrate their first English title for 30 years in an empty stadium as a result of coronavirus chaos.
Liverpool defender Virgil Van Dijk has praised his Egyptian teammate Mohamed Salah, the team's top scorer.
Liverpool moved top of the Premier League standings after beating Brighton and increased the gap to 11 points from second-placed Manchester City and Leicester City.
Liverpool fans celebrated with their defender, Virgil Van Dijk, who won the Men’s player of the year award
Koeman hopes Liverpool pair Virgil van Dijk and Georginio Wijnaldum emerge as Champions League winners on Saturday.
Virgil van Dijk was named Player of the Year by England’s Professional Footballers’ Association (PFA) on Sunday.
Salah returned to his goal scoring form on Friday when he led his team to achieve a 3-1 victory over Southampton.
Last season's runners-up Liverpool dominated Bayern last month, sealing a 3-1 away win after a goalless draw at Anfield to move into the quarter-finals.
The Netherlands will not be lulled into a false sense of security when they face a struggling, new-look Germany in their Euro 2020 qualifier in Amsterdam on Sunday, captain Virgil van Dijk has said.
Van Dijk believes that his Egyptian teammate, Mohamed Salah, is not facing a goal drought and he just needs time to regain his form.