Lennon signed Van Dijk at Celtic in 2013 for just £1.9million from Dutch side Groningen.
The Holland international won back-to-back Scottish Premiership titles and the Scottish League Cup during his two years at Parkhead before joining Southampton in a £13million deal.
He's since become one of the most sought-after defenders in the Premier League, with the likes of Chelsea, Liverpool and Manchester City linked with £70million bids this summer.
And Lennon, currently in charge of Hibernian, believes the 25-year-old has what it takes to play at Europe's top clubs, including La Liga giants Real Madrid and Barcelona.
Neil Lennon says Virgil van Dijk is good enough to play for Barcelona or Real Madrid
Virgil van Dijk has been linked with Premier League's top clubs this summer
Virgil van Dijk tipped to join Real Madrid or Barcelona
When asked if Van Dijk can become the best defender in the world, Lennon told Sky Sports: "Yes.
"I think he could play for Barcelona, I think he could play for Real Madrid – it wouldn't surprise me if he took his career on to those pathways.
"The first day he came into Celtic I pulled him to one side after training and said 'you enjoy yourself here because you're not going to be here long'.
Virgil van Dijk's next club: Where could the Southampton star go next? Tue, May 9, 2017
Where could Southampton star Virgil van Dijk go next? Odds provided by 888sport
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Which clubs are tipped to sign Virgil van Dijk? Odds provided by 888sport
Neil Lennon signed Virgil van Dijk for just £2.2m
"I couldn't believe we got him for €2.2m (£1.9m). He was outstanding. I couldn't believe that none of the big clubs took a bite at him before Southampton.
"I believe he could play at any club side in Europe now – he's that good. He's only 25, he's got 10 years in him.
"He has got everything you want from a modern-day centre-half: he's powerful, he's quick, technically brilliant, he reads the game well, superb in the air.
"So it doesn't surprise me that the big clubs are coming in now – it's just surprising that they have waited so long."