Henk-Maarten Chin claimed the 22-year-old, a top performer for the Parkhead side since his move from FC Groningen last summer, could be on his way to England.
He was quoted as saying: "There has been no official approaches for Virgil yet, but that will come after the season ends. I expect something will happen for him this summer - the intention would be for him to earn a top transfer."
The Hoops boss confirmed that Celtic had withdrawn their appeal of Van Dijk's red card picked up against Aberdeen last month which leaves him sidelined for the Premiership clash with Kilmarnock at Rugby Park on Friday night.
However, not only does he expect to have him back in the side next week, he insisted that it will be down to Celtic as to whether the former Holland Under-21 player will still be in his squad next season.
Lennon said: "I was disappointed with the timing of it and I think Virgil was disappointed too because he had no idea that it was coming.
"It is a bit premature. He is on a three-year contract here. I would guard against that.
"It is not on our horizon, as it were.
"He is one of our best players, we don't need to sell. We have brought him in and put him in an environment where has thrived and prospered, he is our player.
"So whether they want to go or not, it will be down to us to make that decision."
Lennon also admitted his concern about Tony Watt, whose loan spell at Lierse SK took another twist when the striker complained about manager Stanley Menzo, with whom he has had fractious relationship since moving to Belgium last summer.
Watt said: "Whenever we lose I get the blame, and they always say I do things wrong. At Ostend last month I just played for 20 minutes, yet Menzo blamed me.
"I can't score goals if I am sitting on the bench. Menzo has two sets of rules. But you can't have different rules for different players. He clearly doesn't like me."
The former Celtic skipper said: "It is a bit of a worry. It is not the way we want our young players to deal with certain situations.
"I have not been over-enamoured at times with the coach publicly criticising him, I think that can be dealt with behind closed doors.
"I think it is a source of frustration for Tony because he has done okay there, he has weighed in with a few goals during that loan period.
"Maybe I need to speak to him and (tell him to) keep his counsel from here and maybe the relationship will get better.
"But he will be our player again in the summer, I think he has something to offer."
Celtic go into the Killie game 21 points clear of second-placed Aberdeen and on course for their third successive title win in what has again been a one-horse race in the absence of Rangers.
Lennon acknowledged the Light Blues' title win at Ibrox on Wednesday night with good grace but has given no thought to the fact that it represented another step towards a reunion with the Parkhead side.
Rangers clinched the Scottish League One title with a 3-0 win over Aidrieonians with eight games remaining and having won 26 of their 28 matches - with two drawn - and will go into the Championship next season, one title win away from a return to the top flight.
The Northern Irishman said: "It is a good achievement. They have won the league early and they have remained unbeaten.
"It is not something I have given much thought to, to be fair, 18 months (before Rangers could be in the same league as Celtic) is a long time in football but for them to win the league and go unbeaten is very good achievement."