The Southampton defender has been linked with a move to the Reds in recent weeks, while Manchester United, Manchester City and Chelsea have all expressed interest in the Dutchman too.
Saints remain adamant their star defender won’t be leaving this transfer window, especially after selling Jose Fonte to West Ham earlier this week.
But Gerrard, who has recently returned to Liverpool as an academy coach, reckons the Reds could do with bolstering their defence.
Steven Gerrard wants Liverpool to sign Virgil van Dijk
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Who I think we need, I would go and try and bid for van Dijk from Southampton
"Who I think we need, I would go and try and bid for van Dijk from Southampton," Gerrard said on BT Sport.
"But we've had enough of their players so that will probably go down like a lead balloon."
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Liverpool have plenty of history when it comes to transfer dealings with Southampton.
Southampton boss Claude Puel insists Virgil van Dijk is not for sale
Steven Gerrard has returned to Liverpool as an academy coach
Adam Lallana, Sadio Mane, Nathaniel Clyne and Dejan Lovren have all completed moves north of the south coast in recent seasons.
But for now Van Dijk looks set to remain with Southampton, at least until the summer.