His potential had been noted by several sides prior to that move, but the Saints were the ones to take the plunge.
That faith has been rewarded, but Van Dijk’s performances have drawn admiring glances from afar.
Liverpool are among those said to be closely monitoring the 25-year-old, with Jurgen Klopp yet to fully address defensive frailties at Anfield.
Gerrard, who will take on a role as a coach at Liverpool’s Academy in February, told BT Sport: "Who I think we need, I would go and try and bid for Van Dijk from Southampton.
“But we’ve had enough of their players so that will probably go down like a lead balloon."
Southampton have also seen Jose Fonte leave for West Ham during the January transfer window, further depleting their ranks.
They would have been hoping to use Van Dijk in an EFL Cup semi-final clash with Liverpool on Wednesday, but a knock picked up against Leicester City is threatening to keep the Dutchman out of a crucial second leg at Anfield.