Tarrant played 161 games with the Pies before being traded to the Dockers at the end of the 2006 season.
The 30-year-old informed Fremantle officials earlier this month of his intention to return home to Victoria and was a noticeable absentee at the club’s best and fairest awards night on Saturday.
He has been linked to Carlton and Hawthorn, who are in need of quality backmen, but the Magpies are believed to be his preferred option.
Tarrant could opt to nominate for the draft or pre-season draft if a suitable deal can’t be reached.
This tactic worked for the Pies last year when they snared former St Kilda midfielder and now premiership player Luke Ball with pick No.30.
There have also been reports Tarrant could form part of a three-way deal, which would see the defender head to Carlton; Blues ruckman Sam Jacobs go to Adelaide and Crows ruckman Jon Griffin and a draft pick to Fremantle.
Collingwood is yet to declare its interest in the former goalkicker, but is expected to do so in the coming days.
Sports News First also reports the Pies might have to give up forward Chris Dawes or Jarrad Blight to secure the deal, but that the club is likely to shop around more experienced players like Leon Davis, Josh Fraser or Paul Medhurst.
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.
