Van Dijk impressed under Claude Puel at Southampton last season and his form has led to him being heavily linked with a move away from the club.
The Dutch defender has reportedly told Liverpool they are his favoured destination, with Chelsea and Manchester City also interested in his signature.
The Reds will have to stump up over £50million for his signature to fight off interest from their rivals.
Mills thinks he would improve at Anfield but is not worth the fees which have been touted.
Danny Mills says Liverpool signing Virgil van Dijk for £60million would be ridiculous Paper gossip: Liverpool eye £60m Van Dijk move, Chelsea Hazard blow, Tiote tribute Mon, June 5, 2017
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Virgil van Dijk will get better, 25 is a great age
Danny Mills on Liverpool target Virgil van Dijk
"He will get better, 25 is a great age," he said on BBC Radio 5 Live.
"They're going to finish mid-table aren't they pretty much every year.
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Danny Mills says Virgil van Dijk would improve if he signed for Liverpool
"Suddenly now he thinks 'I can go to a top club' and he will improve by going there, by playing with those better players, by playing in the Champions League.
"But £50million or £60million, whatever it is, is ridiculous."
Van Dijk joined Southampton from Celtic in 2015 and has made 55 Premier League appearances, scoring four goals for the Saints.