Brown is entering the final year of his contract at Parkhead and has been linked with a possible summer move to Newcastle.
Although the Scotland international insists he is happy to stay at Celtic, he admits the "pull of the Premiership" could interest him if the right club put up the dosh.
Neil Lennon: "Yes I've heard the rumours.
"We haven't really sat down and discussed anything but Scott knows what we think of him as a player.
"We're hoping negotiations aren't a problem. He is an important player for us, just like a few others, but in his case we would like to get him bedded down because we want him settled.
"He has taken on the added responsibility of being captain and has matured into that role very well.
"His consistency last season was excellent. He was a huge player for us - and considering he's only 25, his best years are still to come."