The centre-half was heavily linked with a move away from St Mary’s during the summer transfer window and he was touted as a target for the likes of both Liverpool and Chelsea.
However, Southampton refused to do business and ended up keeping hold of the Netherlands international beyond the transfer deadline.
It remains to be seen whether any of the Premier League’s top clubs will return with a move to try and sign Van Dijk in the January transfer window or next summer.
However, former England star Le Saux has questioned where Van Dijk would fit in at Chelsea if he were to secure a move to Stamford Bridge.
Speaking to the Daily Star, Le Saux said: “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.”
Chelsea are currently in fourth place in the Premier League table as they look to get back to winning ways in the top flight.
The Blues were beaten 1-0 by Manchester City before the international break to leave them six points behind the leaders after seven games of the new campaign.
Chelsea travel to Crystal Palace in their next Premier League game on Saturday afternoon.
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