Brown’s current contract is set to expire at the end of the season, but the midfielder insists he would be happy to sign a new deal.
Brown told the Daily Record: “I’m happy to say we’re getting close to agreeing a contract extension.
“I’ve said all along I’m settled at Celtic and that I’d love to sign a new deal. Now we’re close and I’m delighted about that. I hope the fans see it as good news too.
“It’s an important year for me. There’s no doubt about it. I’m 26 and no longer the young lad aiming for the breakthrough. I’m getting on a bit now.
“Seriously, hopefully it’s going to be a good season for everyone at the club. We’ve got to get that title back.”