The BBC are reporting that the Saints have contacted the Hoops about the 24-year-old Dutch stopper, although no formal bid has been made.
Van Dijk is believed to be one of a string of defenders on Southampton’s radar.
Ronald Koeman missed out on the signing of Belgian defender Toby Alderweireld last month while Romanian centre half Flordin Gardos faces seven months on the sidelines after sustaining a serious knee injury, while youngster Jordan Turnbull has been farmed out on loan to Swindon Town.
And Koeman is on the look-out for defensive reinforcements, with Jos Hooiveld’s departure to AIK Stockholm leaving the former Netherlands international with just Maya Yoshida, Jose Fonte and summer loan signing Steven Caulker as his central options.
Van Dijk has been linked with a number of clubs in recent months, including Everton, Arsenal, Norwich and Spurs as well as a handful of clubs in Germany and Spain.