Both parties are expected to sit down soon to discuss a new deal but Brown can speak to other interested clubs as of Thursday.
However, Lennon believes Brown is fully committed to the Glasgow club and expects contract discussions to be smooth.
“The club was due to meet his representatives on Tuesday, but they had to cancel,” Lennon told The Times.
“But I have spoken to Scott and he says there has been no contact with any other clubs. He also said he is quite happy to stay and sign a new contract.
“He can talk to other clubs now and we can’t stop him from doing that — but I am not convinced he will.
“I certainly don’t get the impression he is leaving. He has told me he wants to stay and we have put the contract in front of him.
“There is just this matter of getting the problem sorted out, and it has dragged its heels a little bit.”
However, Lennon did admit the constant speculation over the 26-year-old's future was growing tiresome.
“It is not irking me, but I have to keep answering questions about it, and I want it resolved sooner rather than later,” he said.
“But I still think it will be resolved the way we want it to be.”
Brown received a lukewarm reception from the home fans on Wednesday night but Lennon believes the issue will go away once the new deal is signed.
“If Scott decides not to sign the contract, he might get an adverse reaction from some supporters,” Lennon stated.
“But, until that point comes, I think the supporters are right behind him.
“I think we missed him at times when he was out. If you look at his playing record since I have been manager, we have won more games than not when he has been involved.
“I don’t want any headlines saying that I am selling Broony. That is not the case at all.”
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