The 23-year-old has been widely tipped to succeed Brown at Celtic Park.
Speaking to the Daily Record last month, McGinn's old Hibs boss Alan Stubbs said the 23-year-old would be a 'ready-made replacement' for Brown at Celtic.
But while McGinn - who was linked with a move to Celtic Park earlier this year [Express] - has insisted he is not looking to take the 32-year-old's place, he admitted he would like to play alongside his international teammate.
"[Replacing Brown] is not something that I think about," McGinn told the Evening Times. "We are different players. Scott has been the driving force for Celtic and Scotland for a long time.
"We are different players entirely; he has a right foot, I have a left foot for a start. I try to take wee bits from his game and implement it into mine but at the same I try to take bits from others too - Darren Fletcher, Callum McGregor, Stuart Armstrong.
"I don’t try to base my game on one player and I would rather play alongside him than replace him.
"I have had nice wee tussles when I’ve played against him but you want to show you can match him. If I can have as good a career as he has had in a Scotland jersey I’ll be delighted."
McGinn has also had interest from south of the border since helping Hibernian back to the Scottish Premiership this summer.
However, the former St Mirren player's Glasgow ties, not to mention those between his family and Celtic Football Club [McGinn's grandfather, Jack, is a former Bhoys chairman], could give Brendan Rodgers' side the advantage should he ever leave Easter Road.
He is unlikely to come cheap, though, with Hibs boss Neil Lennon telling STV earlier this year McGinn is worth 'a lot more' than the £5 million widely quoted.