Dutch representative Henk-Maarten Chin revealed the centre-half was being closely monitored by several Barclays Premier League clubs earlier this week.
The 22-year-old defender has been outstanding for the Scottish champions since sealing a £2.6million move from Groningen last season.
But Lennon stressed that Van Dijk is under contract and it would take a sizeable offer for them to agree to part company with him.
"He's our player and is on a three-year contract," said the Celtic manager.
"I get really frustrated with this scenario. We bring in a good player and then everyone is trying to sell him off after six months or a year because he's playing in Scotland or because England is just over the road.
"He's on a three-year deal and we're in no rush to sell and there is no need to sell. It's very premature.
"Virgil was very disappointed and according to the agent there were some quotes taken out of context, but I haven't spoken to him and so I can't verify that.
"He isn't itching to leave at all. Yes, every player has their price as well, but we'd be looking for quite a sizeable fee for Virgil."
Lennon added: "It's understandable there's interest because he's a quality player and one of the best I've had here in the four years I've been here.
"We liked the look of him as soon as we saw him. I saw him in the Europa League play-off game and immediately thought he'd be a good signing.
"And that's proved to be the case. He's been faultless in more or less every game and his attitude has been fantastic. His application to training is fantastic as well."
Lennon admitted he was speaking to Celtic chief executive Peter Lawwell and major shareholder Dermot Desmond about strengthening for next season.
He said: "Talks have been trotting along now for a few months. I don't know what will happen with Virgil. We've had no indications from other clubs and no offers.
"Looking at him, he's happy. I'd be second-guessing things, but we've had no approaches so far.
Meanwhile, Lennon expects the SPFL Premiership leaders to extend Kris Commons' contract for another season when it expires in the summer - and then look to tie him up on a long-term deal.
He said: "We're talking about a top, top player here. A Player of the Year candidate, no question.
"He's been so consistent this year. We've got a few - Fraser and Virgil have been a model of consistency as well. So we should have a few contenders."