The Magpies will reportedly come in with a £6million bid for the Scotland midfielder but the Hoops are loathe to lose him and will offer a new and improved long-term deal.
It is believed that Brown is keen to stay at Celtic Park and will be more than happy to sign a new deal but only if manager Neil Lennon is also offered a fresh contract.
A close friend of Brown’s told SunSport that the Hoops skipper is very happy in his current environment.
"Scott knows he could probably go down south and get a lot of money. But the fact is he's absolutely loved it under Neil, he's made no secret of that,” said the source.
"He's also made it clear he is the only man for the job at this moment in time.
"Scott is happy in Glasgow and really enjoying his football. He already had initial talks about a new contract a few weeks ago and if a deal was put in front of him then I think there would be no doubt he would be happy to sign it."