In the latest episode, Spanish captain Ramos has chosen to click on the "like" button to a user's image mocking the Croatian defender. On the flip side, others have tended to criticise the 32-year-old's occasionally aggressive conduct.
Van Dijk told Dutch outlet De Telegraaf: "Ramos is not the best".
He is a great player and I respect what he has achieved but he is not the best, he is not my type of central defender.
Ramos' rather unorthodox defensive style has established the Real Madrid hero as a largely divisive figure, with his discipline and solidity in defence often leaving much to be desired.
But, as with most things in life - and certainly most things on Twitter - it came back to bite the Liverpool defender right where it hurts when England beat Croatia 3-2 at Wembley on Saturday, going through to the Nations League finals and dumping Croatia out.More news: YouTube Is Showing 'Terminator,' 'Rocky' and Other Movies for Free
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Lovren, who insisted that he's one of the world's best defenders after Croatia reached the World Cup final in Russian Federation, caused a further stir earlier this week by taking another pop at Ramos following his national team's 3-2 victory over Spain in the UEFA Nations League. "I try to avoid the situations he gets into, and don't even try to make slide tackles".
The former Southampton star has become the defensive bedrock of Liverpool since completing his £75m move to Jurgen Klopp's side from St. Mary's in January.
The origin of Lovren's dispute with Ramos appears to go back to the Champions League final in May when the Madrid defender's robust challenge on Mohamed Salah ended the Egyptian's participation in the match.