Liverpool tried to take the Southampton defender to Anfield in the summer but had their approaches knocked back.
Saints went as far as reporting Liverpool to the Premier League alleging the Holland international had been tapped up.
But Henry, who was watching the baseball team he owns in Boston, has been urged to give it another try in January.
A 19-second video of the heckling has been posted on Twitter.
“Sign Virgil van Dijk in January,” the fan shouts. “It’s the right thing to do.
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“Van Dijk in January. It’s the right thing to do. He wants to play for us.”
Van Dijk is yet to play this season after handing in a transfer request in an effort to force through a move.
Chelsea, Arsenal and Manchester City were also interested but Liverpool were believed to have been the 26-year-old’s first choice.
But, after signing a new six-year deal last season, Saints stood firm and refused to sell.
Having missed out on signing Van Dijk Liverpool decided to stick with what they have in defence and have struggled.
They were thumped 5-0 by Manchester City last weekend and shipped two against Sevilla in the Champions League.
They have conceded eight times in the Premier League in just four games – with only West Ham having shipped more, although Arsenal, Leicester and Bournemouth have also let in eight.