The Scotland midfielder has been loosely linked with English Premier League outfit Newcastle United this summer but it seems certain he will remain at Parkhead and Lennon is confident a new deal can be sorted soon.
"We have not sat down and discussed anything but Scott knows what we think of him as a footballer,” Lennon said.
"We're hoping negotiations aren't a problem.
"He's an important player for us, just like a few others - but in his case we'd like to get him bedded down because we want him settled.
"He has a year left on his contract so it's very important we negotiate pretty quickly."
And Lennon had some extra praise for Brown after he came off the bench to score the winner just over 10 minutes from time in their final Australian tour match against Melbourne Victory on Wednesday.
"There is far more to his game than just passion,” he added.
"He lifts the team by the scruff of the neck at times and considering he's only 25, you have to wonder how much better is he going to get.
"He is not even at his peak and I honestly think his best years are still to come."