Van Dijk is set to undergo surgery and will miss the majority of the season after suffering a knee injury during Liverpool’s 2-2 draw with Everton last Saturday.
Fabinho deputised for the Dutchman on Wednesday evening as he played alongside Joe Gomez at the heart of Klopp’s defence against Ajax.
The Brazilian impressed against the Dutch side as a Nicolas Tagliafico own goal in the first half sealed a 1-0 victory for Liverpool in their Champions League group-stage opener.
Speaking after the win, Fabinho revealed that Klopp is keen for him to be the organiser in Liverpool’s back line whilst Van Dijk is sidelined.
‘Personally, when I knew Virgil was out for a long time it was a little bit of a shock because I think he’s the best defender in the world,’ Fabinho told Viasport.
‘Most of all, he’s a leader of the team, in the dressing room he always keeps the good mood, the good atmosphere, and of course we miss this.
‘But we have to keep going, we have to try to do the best and win the games for him as well.
‘We have Thiago, Alisson, Joel [Matip], some players injured right now, they try to recover as quickly as possible and we have to try to win every game.’
Asked how his role will change if he becomes a regular at centre-back, Fabinho replied: ‘Tactically, I have to be always ready for the long balls, try to organise the team.
‘It’s not easy but I have to do what Virgil always does and talk to the team, try to be a leader.
‘It was very important for me and the team to keep a clean sheet today for the confidence of the team.
‘Of course, I try to do my best, the manager said to me I have to talk more to the team to try to organise the team.
‘Sometimes it’s little details like second balls, being ready, pressing well. I try to be in this role as well.’