Lennon revealed the contract offer had been on the table since October, while the bid from Norwich was slightly improved on one submitted late last week.
Lennon told BBC Radio Scotland: "We have had an improved offer, if you want to call it an improved offer, from Norwich that's been turned down automatically."
Lennon did not want to go into details about Norwich's offer but said it was not much more than the original figure.
When asked if it was £6million, Lennon said: "It was nowhere near six million. It was completely rejected and even if it was six million it would be completely rejected."
Lennon claimed little had changed with the situation of the striker, who has 18 months left on his deal.
When asked about reports that Hooper had rejected the club's latest offer, Lennon said: "It's not the latest offer because we made it two or three months ago.
"I'm disappointed again that these things have come out in public. I'm not too sure where they are coming from but it's certainly not us.
"It's as you were. He didn't like the look of the contract two or three months ago and nothing has changed.
"We feel it's a very good offer. It would put him in the top two or three highest-paid players at the club. I'm sure he wants to be the highest paid but you can't always get what you want."
Celtic paid Scunthorpe around £2million for Hooper in the summer of 2010, but Lennon claims he cannot see chief executive Peter Lawwell and the board cashing in on the 24-year-old this month.
"Not as far as I can see it," Lennon said. "We are very solid on that, myself, the backroom staff, Peter and the board."
Lennon, who picked Hooper in the starting line-up for his side's Clydesdale Bank Premier League clash with Dundee United tonight, added: "Come February 1, the contract offer will be withdrawn.
"They have got a lot to think about, Gary and his representatives.
"If he doesn't want to sign the contract, that's his decision. It wouldn't be my advice, but it's Gary's decision, or his representative's decision.
"We are quite comfortable with that and we respect that.
"We made this offer in October and all of a sudden it has been rejected. It's no coincidence that it's the last 10 days of the (transfer) window, but we are quite comfortable with the whole situation.
"I'm pretty sure Gary will be a Celtic player come February 1. We have had private chats and he is really happy here. He wants to stay, he wants to see out the season, and we will have a look at the situation then."