Tarrant is seeking a return to Melbourne, preferably with his original club Collingwood, but the Hawks have been strongly linked to him.
Hawthorn general manager player personnel and strategy Chris Pelchen says the club would love to have Tarrant on board.
"There's genuine interest there, there's no doubt, but Paul Connors his manager has explained he'd like to go to Collingwood and we've respected that at this point in time," Pelchen said as he arrived at Etihad Stadium for the commencement of trade week on Tuesday morning.
Pelchen said it was unlikely the Hawks would be part of any early trades.
"It wouldn't be this early. We've had discussions with all clubs except St Kilda to this point and it would be fair to say it's very preliminary," he said.
"We might know a bit more in about six hours, we've got a couple of clubs we want to ask about but it better remain private until later in the day."
Pelchen said there was no one specific player type the Hawks were after.
"There are probably several. Obviously to improve our list is the main objective. We're looking at midfielders and obviously backmen, that is widely known," he said.
"We haven't discounted any player position provided that improves our club."
Bulldogs coach Rodney Eade says his club is interested in Lion Justin Sherman and Cat Nathan Djerkurra while Andrejs Everitt was looking to leave Whitten Oval.
"Andrejs has indicated that he'd like to go, but at the same time he's under contract so we'll certainly be happy to keep him. It depends on what other teams [offer]," Eade said.
New Essendon coach James Hird said he was not looking at taking any drastic action in his first trade week at the helm.
"Look, we're just going to have a listen, really - we've had a good look at our list, but we're just going to listen to what other clubs are saying and take it from there," Hird said.
He confirmed that he had talked to disgruntled midfielder Bachar Houli, who has been linked with the Tigers, and told him he was still wanted at the Bombers, and said he was happy that Brent Stanton and Leroy Jetta were now more inclined to stay now he had taken over.
Follow our complete coverage of the 2010 AFL exchange period from October 5-11. No trades are official until paperwork has been accepted by the AFL and formally recognised after 2pm on Monday, October 11.
Join the AFL trade conversation on Twitter: use #tradeweek in your tweets
