The Premier's office confirmed talks were held via a statement released on the Government's website on Friday.
Hawthorn is currently in the final year of a five-year, $15 million deal that has seen the club play four home games a year at Aurora Stadium in Launceston. A renegotiation and extension of that deal remains the Tasmanian Government's priority, but Premier Bartlett will not spurn advances from other AFL clubs.
"We are prepared to hear what other clubs and the AFL are prepared to offer Tasmania," Bartlett said.
"It is clear that other clubs are interested in playing games in Tasmania and the AFL supports that. We welcome that interest, but the Government has made no commitments nor had any formal proposals put to it.
"If the AFL or other clubs want to stage games at Bellerive, we are not opposed to that."
North Melbourne and Melbourne have also been mentioned as possible suitors if a suitable deal can be struck.
The AFL has given cautious approval to the idea, but any concrete announcements are still some way off.
"The AFL's position is that it has had initial discussions with the Tasmanian Government regarding the possibility of games at Bellerive Oval," AFL spokesman Patrick Keane said on Friday.
"It has also had preliminary discussions with several of our clubs. These talks are in the early stages, and will proceed in the coming weeks.
"Any announcement on whether some games may be played at Bellerive in the future is not expected before the latter part of the season."
