As is his policy, Lennon refuses to confirm reports from England that the Huddersfield midfielder - who started his career at Manchester United and is now a Northern Ireland international - is on his wanted list.
However, the Hoops boss did admit: "We have watched Huddersfield twice, and he is a player who has shown up well in the two games I have seen. But there is no offer in the offing at the minute."
Lennon has also been linked with an interest in 22-year-old Norwood's team-mate, striker James Vaughan.
But the asking price for the former Everton hitman - bidding is expected to start at £5million - looks like pushing him outwith Celtic's signing strategy.
Left-back Paul Dixon - who moved to Huddersfield from Dundee United 18 months ago - is another at the English Championship side reported to be under consideration by the Scottish champions, though Lennon said there was nothing in this link to the 27-year-old.
Lennon has, however, confirmed he wants cover for Emilio Izaguirre, and that he is also looking to strengthen the options for central defence.
More than £20m has been generated from player sales in the last couple of years. And, while Lennon said it would take the same amount to replace like with like, he accepts he will not be handed anything like such a sizeable war chest.
But he is continuing to look for the next player who can be developed.
A decision is set to be made on Japanese midfielder, Hiroki Yamada, while Egyptian rising star, Mahmoud Hassan, is claiming his club, Al-Ahly, have already turned down an offer for him.
Lennon insisted he knows nothing about this, nor about speculation he himself could be a target for managerless West Brom.
He also made light of Zlatan Ibrahimovic's revelation the giant Swedish striker would like to finish his career in the Hoops.
The Celtic manager is serious, however, about facing a very busy month trying to bring in the extra quality he believes the players already at the club deserve to help them put a silver lining on the season and prepare for another crack at the Champions League qualifiers.
He said: "I want to keep the players I have, add to the squad and make it better.
"I think we deserve it, and I think the players deserve it as well.
"They want to see a bit more quality coming in to make 2014 another good year to look forward to."