The Roos’ current deal to play two games a year in the south of the state expires next year but could be beefed up to include up to three games in 2016 and beyond.
"We really had to twist the AFL's arm to get two games initially," Brayshaw said after arriving in Devonport on the Spirit of Tasmania.
"We've talked to them about the possibility of three and they were very positive about that providing it could be done.
"Beyond that, with the Hawks playing four, that's seven home games played outside of Melbourne.
"I think it is about the limit when we are dealing with the current quota."
One thing that may change all that, is the fact the current quota for MCG and Etihad games expires in 2016, which is also the last year of Hawthorn's contract with Tasmania.
AFL Tasmania wants just one team to play eight home games between Launceston's Aurora Stadium and Hobart's Blundstone Arena, but Brayshaw said North had not been involved with the concept.
"Our stated aim is to engage with southern Tasmania and the magnificent city of Hobart and play two and if we can three games at Blundstone [Arena], which we think is a phenomenal venue, and honestly we don't look beyond that."
With the AFL fixture set to be released in the next two weeks, Brayshaw revealed North had requested an all-Melbourne match in Hobart.
"I would love it to be a Melbourne club, like a St Kilda or Melbourne or a Western Bulldogs, would be fantastic, but what we ask for and what we get are poles apart as a rule," he said.
"Having said that, you only need to see the rise of the Gold Coast this year.
"If they were scheduled to play a game at Blundstone Arena, it would be a fantastic game of footy."
North Melbourne held a board meeting aboard the Spirit of Tasmania on Tuesday night.
