The Dutch defender spent much of the summer being heavily linked with a move to Anfield, with the Saints accusing their Premier League rivals of making an illegal approach at one stage.
Eventually the deadline passed with no deal being done, forcing Van Dijk to stay put and put any potential distractions to the back of his mind.
Transfer talk is, however, building again ahead of the January window and former Liverpool cult hero Kuyt believes a fellow countryman would be a hit on Merseyside if interest is rekindled.
He told Sky Sports News on the ongoing Van Dijk rumours: “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.
“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.”
Jurgen Klopp’s decision not to bolster his options at centre-half during the last window has been discussed at great length, with the general consensus being that greater squad depth is required.
Kuyt is among those in that camp, with the ex-Netherlands international aware of the need to have more than just a strong starting XI.
He added: “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.”
The Reds have been inconsistent at times this season, leaving them 12 points adrift of Manchester City in the Premier League title race, but they are very much in the mix for a top-four finish and are closing in on safe progress through to the last-16 of the Champions League.