Former Southampton forward Austin claimed he couldn't believe United's decision to turn down van Dijk, who has now won the Premier League and Champions League at Anfield.
Austin, currently on-loan with QPR, told talkSPORT: "I remember in the back end of his Southampton career, we were on the bench at Chelsea away. I was sat there (and said): 'Come on Virg, what's going on? Surely Man United must have been in for you? It's a massive club in England'.
"And he said: 'In the summer it was between me or Lindelof. And they signed Lindelof. No-one knows that'. I couldn't believe it. I was gobsmacked.
"There was talk in the summer about whether he was going to go there and they've gone and taken Lindelof instead."