Brown laughed off comments from Barton that he was “not in the same league” as the former Newcastle, QPR and Burnley midfielder, who had previously declared his affinity for Celtic on Twitter, years before joining Rangers.
Speaking at a press conference to promote Celtic’s International Champions Cup tie with Leicester on July 23, Brown said: “I’ve not been in his league. He’s in my league.
“I think we’ll get on really well, him being a Celtic fan. So I think we will get on great. The Rangers-Celtic games will be good.”
When asked if the comments fired him up, Brown said: “I hear that every day. It’s part and parcel of football.”
Brown failed to mention newly-promoted Rangers after being asked about what competition the champions expect to face this season.
“I think Hearts and Aberdeen have done great in the last couple of seasons,” said the Scotland midfielder, who declared himself fully fit after being troubled by hamstring problems towards the end of last season.
“They have challenged us all the way, and I think they are going to do the same.
“I think it’s going to be hard to see past Aberdeen. It’s always hard and we have struggled going up there last season, so hopefully we can do a lot better this season.
“Hearts are a great team, strong and physical. But we have a new manager and a fresh start and we will show what we can do.”