That’s the verdict of former Blues man Graeme Le Saux, who reckons Antonio Conte’s squad is already well-stocked in defence.
Van Dijk, 26, emerged as a target for a cluster of top Premier League sides at the start of 2017.
And while a move to Liverpool was believed to be preferred by the centre-back over the summer, Chelsea remained a potential destination towards the end of the transfer window.
This week Van Dijk admitted he’s still interested in quitting Southampton and that he will see what happens in January.
Le Saux, who used to play left-back for Chelsea, reckons the Holland international would have to battle for a place in Conte’s team if he headed to Stamford Bridge though.
Le Saux told Starsport: “If Chelsea are to carry on with playing a back three then they need top quality players in those positions but [Gary] Cahill, [David] Luiz and [Cesar] Azpilicueta are all having decent seasons so far.
“In addition, [Andreas] Christensen has done well having come through the ranks so I think Van Dijk would have quite the fight on his hands in trying to displace those players from the starting XI.”
Le Saux identified the position Chelsea should be looking to strengthen going forwards.
“The bigger issue for me is the need for a strong back-up option to Marcos Alonso,” he added.
Chelsea return to Premier League action against struggling Crystal Palace on Saturday October 14.
Conte’s men are fourth in the table having picked up 13 points from their opening seven games.
Pirlo coy on Chelsea links
Andrea Pirlo has refused to rule out joining Chelsea’s coaching staff following his retirement from playing.
The Italian midfielder, currently with New York City, confirmed on Sunday that he will conclude his career at the end of the current Major League Soccer season at the age of 38.
Pirlo played under Antonio Conte for both Juventus and Italy during a superb playing career which saw him win six Serie A titles, two Champions Leagues, and a World Cup.
And he was coy when asked about speculation of a reunion with Conte at Stamford Bridge.
“My future, I don’t know yet. I will return to Italy in December,” he told Gazetta dello Sport.
“An assistant to Conte? People are saying that. I have my ideas but I need time to decide.”
Pirlo has spent the past three years in New York but has featured in just 15 of the club’s 32 games this season.