The Merseyside club were keen on signing the Dutch international earlier in the transfer window. However, the Reds were forced to end their interest in the centre-back in June after they issued a public apology for any "misunderstanding". There were suggestions that Southampton were planning to report Liverpool to the Premier League for an alleged illegal approach.
Van Dijk is unhappy with the current situation as he continues to be linked with a move to Anfield, while the Premier League winners and Pep Guardiola's side have also maintained interest in the player.
There are fears that Van Dijk could leave St Mary's Stadium this summer and Dunne has urged the central defender to prefer Chelsea to Liverpool.
"I think he is very good. If he has the opportunity to go to Chelsea, then they are the stronger of the two, so I think he should go there," Dunne told talkSPORT.
"He would suit playing three at the back as well. It's disappointing the way things have worked out for him over the summer and he is being forced to train alone, but over the next couple of weeks [you'd think] he will get his move."
Southampton's new manager Mauricio Pellegrino revealed the 26-year-old has been omitted from the squad for the club's pre-season trip to France. The Saints boss stressed Van Dijk is not psychologically fit to train with his teammates.
"Now he is not involved with the team because psychologically he is not 100%. If you are not 100% with the team I need to work with the players who are 100% to defend Southampton. It's easy for me," Pellegrino explained.