Franklin is out of contract at the season's end and is in the Giants' sights. Reports suggest the AFL's newest club will offer him a massive deal over six years.
Despite the fact Franklin would become the Giants' marquee player and a marketer's dream, Demetriou said it would make"a great statement" if the dual Coleman medallist stayed a Hawk.
"I am a traditionalist at heart and I actually like seeing players play at the club they started at," Demetriou told Fox Footy's AFL 360.
"For the good of the game it would make a great statement if Buddy Franklin stayed at Hawthorn."
There have been suggestions Franklin could be paid extra by the AFL to head north and be an 'ambassador' for the game.
But Demetriou said Franklin could also be an 'ambassador' and stay at Hawthorn.
"Any player, and we have several players who get paid for ambassadorial roles in the competition, we have multicultural ambassadors," he said.
"They get paid based on the work that they will do and what they're going to put in.
"I have absolutely no idea whether Buddy Franklin is interested at all in being an ambassador.
"If he wanted to be an ambassador for football in Melbourne, we would sit down and talk to him.
"To the best of my knowledge, he may not want to be involved in an ambassadorial role."
Demetriou said suggestions Israel Folau was paid $1million by the AFL for his ambassadorial work with the Giants was incorrect.
Jennifer Phelan is a reporter for AFL Media. Follow her on Twitter @AFL_JenPhelan.