The Celtic boss had hoped the 22-year-old, who is free to leave the club in the summer, would put pen to paper on an extension to his current deal.
However, the Norwegian defender, who has not been a regular starter this season, has rejected the offer. Lennon, though, has urged the defender to remain in Glasgow and fight Efe Ambrose, Charlie Mulgrew and Kelvin Wilson for his spot.
Lennon said: "Thomas is a good player and we would like to keep him at the club beyond the end of the season. But I think he has to be patient.
"Efe, Charlie and Kelvin have all done exceptionally well for us in his position this season. But Thomas has always done a job for us when he has come in.
"We had offered him a contract and he has turned it down. We may go back to him with another offer, but there are no guarantees on that front."
Meanwhile, the Celtic boss has revealed that Gary Hooper has moved to a new agent – but predicted there would be no change in the striker's situation.
The Hoops, who turned down several multi-million bids for the Englishman from Norwich City last month, have offered a new deal to the prolific hitman.
Lennon said: "His contract with the guy he was with ran out in January. But it is as you were with him. The contract (offer with Celtic) is still there.
"They have not intimated to me that he is going to sign a new contract. I'm assuming they will look at things in the summer. It's up to them to come back to us."
Meanwhile, Lennon will find out early next week if Celtic captain Scott Brown needs to undergo surgery on a persistent abductor injury.
However, if the Scotland midfielder does go under the knife, he will not be ruled out for the remainder of the 2012/13 campaign.
Lennon said: "I don't think he will be out for the rest of the season. An operation like that normally requires four to six weeks out."
Right-back Mikael Lustig will miss Celtic's game against Dundee at Parkhead tomorrow afternoon due to bone bruising.
Charlie Mulgrew is also doubtful, with a slight glut strain. Georgios Samaras, though, has returned to training and is expected to be in the squad.