Tarrant, who spent nine years at the Magpies before joining the Dockers, is desperate to return home and run around in black and white in 2011.
But negotiations between the clubs are progressing slowly at this stage, which has opened the door for Tarrant to enter the draft.
That would result in Fremantle getting no compensation for losing him.
"He'll be worth whatever Fremantle can get for him, because if they don't accept that he will go in the national draft," Connors told afl.com.au's Trade Week Radio on Friday morning.
The Dockers are currently trying to get a third club - believed to be Adelaide - involved in the deal as they try to secure a more palatable outcome.
But Connors is also urging them to consider a player swap.
"Jack Anthony, I heard, is looking for a new home," Connors said. "There's Leon Davis. I've got a young kid by the name of Jarrad Blight looking for a new home."
Connors believes Tarrant can have a great impact for the Magpies if he can get back to the club.
"Chris had nine years at Collingwood and he just feels that he owes them a couple of really good years at a place that he can call home," Connors said.
"You saw it with Trent Croad [who went from Hawthorn to Fremantle and back to the Hawks] and Chris has looked at that.
"He's got some very good friends at Collingwood, he's matured, and he's really looking forward to playing there next year.
"Chris has done all right out of footy and he's got a really good business to jump into, but I think he's got some really good years of footy ahead of him.
"I think you can play [Nathan] Brown, [Ben] Reid and Tarrant in the same side. The Magpies want to be able to stay in premiership mode even if Reid or Brown goes down with an injury."
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.
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