The defender's agent was quoted earlier in the week as saying there were English clubs interested in signing the 22-year-old and that he expected "something will happen for him this summer". Van Dijk, who is suspended for this evening's SPFL Premiership match against Kilmarnock, joined Celtic from Groningen last June.
"He's our player and is on a four-year contract," Lennon said. "I get really frustrated with this scenario - we bring in a good player and everyone is trying to sell him off after six months or a year because he's playing in Scotland or because England is just down the road.
"We're in no rush to sell and there's is no need to sell. It's very premature. Virgil was very disappointed [with the story] 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. We've had no indications from other clubs as yet and no offers. Looking at him he's happy. I'd be second guessing things but we've had no approaches so far."
The Celtic manager added: "Every player has their price but we'd be looking for quite a sizeable fee for Virgil. [Reported interest] is understandable, though, because he's a quality player and one of the best I've had in the four years I've been here. 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. I don't know how much better he can get as he has everything you would want in a modern-day centre-half. He's quick, very good in the air and superb with the ball at his feet. The fact he's not playing against Killie means we have to try to replace his presence. He'll be missed. He's only 22 so there is more scope to develop but there are not many faults in his game at the minute."
Van Dijk will not be Celtic's only first-team figure missing from tonight's contest at Rugby Park. A groin strain will keep Nir Biton on the sidelines for the next month, and James Forrest will also miss out with a similar complaint.
It is the latest in a long line of problems for the young Scot and something Celtic hope the 22-year-old will eventually grow out of but for the meantime they are doing all they can to manage the player's lifestyle to try to keep him fit and healthy. His car was assessed to see if that was a possible contributory factor, and Forrest's commute from Prestwick to Lennoxtown was eliminated when he elected to move.
Lennon regards Forrest as a "sensational player" on his day, the only problem being that he is not able to use the winger's services more often. "James picks up these injuries sporadically," added the manager. "It's just his mechanics. You're hoping that [it stops] when he fully matures but at the moment it's just niggle after niggle. He's just so bulky around the pelvis and thighs that he's just prone to picking up these strains.
"He had a long-term problem with sciatica and so he's doing a lot of work in between games to keep that at bay. But he's getting different injuries as well. We seem to have got to the bottom of the sciatica problem but he's always been prone to picking up little hamstring and groin strains. We just hope that isn't going to be the case throughout his career. A fit James Forrest is a huge asset for anyone so we hope he will grow out of it.
"Early in his career Ryan Giggs had a few problems because he was so quick and finely tuned. James has played a lot of football early in his career as well. Players tend to manage things better as their bodies mature and their careers go on.
"We looked at his car at one point to see if that was a factor, plus the fact he was living in Prestwick with an hour-and-20-minute drive to training and back every day. But now he lives closer to the training ground. We're looking at all avenues to see if we can prolong him for an injury-free period.
"He's a sensational player, we've just not seen enough of him on the pitch. That's not his fault. We've missed him in some big games. We'll do everything we can to look after him as he's a precocious talent."
This is Celtic's first Friday night game since they played Motherwell in early December, their 5-0 win overshadowed by the damage caused to the seats in the away end of Fir Park. "I'm looking forward to it and hope we play as well as we did the last time out," Lennon added. "I think the atmosphere's a bit better. I know we had a few problems at the last one but I'm pretty confident there won't be a repeat of that."