The Hawks have taken fixtures to Launceston's University of Tasmania Stadium for more than two decades and boast an impressive 75 per cent winning record at the venue.
They added another notch to their belt with a 12-point win over the Giants on Saturday night to maintain their unbeaten start to the season.
Tasmania Devils CEO Brendon Gale has said his preference is to not share the state with Hawthorn when his side enters the league in 2028.
Hawthorn in February extended their deal to play four games a year in Launceston until the end of 2027.
But Mitchell hopes the arrangement can be extended.
"My personal view is it makes perfect sense. We've been coming here for over 20 years now," he said.
"We certainly feel at home here. To play against them (Devils) on a regular basis, to play probably here (Launceston), I think it makes perfect sense.
"Hopefully we can continue to keep some relationship with Tasmania because we've worked so hard and Tassie has embraced us in such a fantastic way for such a long period."
Mitchell said he understood Hawthorn CEO Ashley Klein was working "pretty hard" with the Tasmanian government to make sure the club could remain part of the landscape.
"I hope they can work something out. I think we add value to the Tassie people, and (they) certainly add value to us," Mitchell said.
The Devils plan to split home games between Launceston and Hobart, initially at Bellerive's Ninja Stadium until a new 23,000-seat waterfront venue is completed.
Since the Devils' official launch in March 2024, junior participation in Tasmania has grown by some 40 per cent, according to the club.
More than 14,000 people packed University of Tasmania Stadium, close to the ground's capacity, on Saturday.
The venue, considered to have one of the best playing surfaces in the AFL, will undergo a $130 million upgrade expected to be finished by early 2027.
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