Liverpool pursued Van Dijk as a priority target early on during the summer transfer window but formally ended their interest after Southampton threatened to report the Reds to the Premier League over an alleged illegal approach for the player.
Reds owners Fenway Sports Group assured Southampton that they would not make any further approach for the player unless they were invited by the south coast club, but recent reports have suggested that the Merseyside club will launch a fresh attempt to sign the £60m ($79m) rated defender in January.
Kuyt backed his compatriot to do well at Liverpool if he ends up moving to Anfield in January.
"I know Virgil. I didn't play with him in the national team but he's a great player. We'll see how things will go in the winter break or at the end of the season," the ex-Feyenoord striker told Sky Sports.
"I don't think it's strange for me to say he is a player who will suit Liverpool very well. He has the right mentality and he is a great defender.
"He could do a great job at Liverpool but it's not for me to say if he would be an improvement or not. That's up to the club."
Kuyt went on to say that Liverpool did not have a strong enough squad to challenge the likes of Manchester City and Manchester United for the Premier League title.
"I think the Liverpool team now has great players but if you want to be contenders for titles then you have to have more than 11 good players," he said.
Klopp's side are preparing to face Sevilla in the Champions League group stages on 21 Novemeber.
The Reds will be assured of progression to the knockout stages with victory at the Ramon Sanchez Pizjuan.