The former Geelong veteran, who was told the Cats wouldn't offer him a new contract last month after 198 games and 13 seasons, is optimistic after a positive meeting with the Giants.
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The 31-year-old has no on-going issues with his body and feels in good shape after playing just 12 games this season.
He will now wait to see if the Giants will offer him a lifeline, as they have with Chad Cornes, Dean Brogan, Bret Thornton, James McDonald, Luke Power and Setanta O'hAilpin in the past two years.
"It went fine. It was just a quick once-over from them, a medical, and I don't know what the go is yet any more than that," Hunt told AFL.com.au on Thursday.
"It was sort of a way for them to suss out what I was thinking and for me to ask any questions.
"There are no issues. I didn't play a whole lot of footy last year either so I feel pretty fresh actually.
"I'm still just in the same sort of boat until I hear anything from them."
Hunt has continued to train and keep himself fit after being told he would not continue with Geelong a week after the Cats' preliminary final loss to Hawthorn.
He is back in Geelong after Monday's meeting and has been spending time with his family while he waits to see if an offer eventuates.
While Hunt believes the meeting with the Giants went well, he is realistic enough to know it might not amount to a second chance.
"I've never been in this boat before but I've been in the industry long enough to know that footy's a funny game.
"The minute you think things are going all right they tend to turn on their head a little bit.
"I went up there with an open mind and they were great, so there's really not a whole lot to say until I hear back from there."
Hunt is yet to field interest from any other AFL clubs and has kept an NFL venture in the back of his mind, following on from his friendship with former Geelong player and NFL punter Ben Graham.
But he doesn't want to explore that possibility until he is sure his AFL career is over and hopes the Giants find a role for him in the wake of the retirements of Cornes and Brogan and departures of Thornton and O'hAilpin.
"They've lost some experienced blokes this year and they've moved on to roles in the footy club," he said.
"They've lost a lot of experience and they've gained Shane Mumford, and Heath Shaw has said that's where he wants to be.
"They've got some experience but I feel hopeful they can find a spot for me."
Hunt hopes to hear from the Giants in the next few days one way or another after the meeting, which he said didn't involve talks about terms or money.
He said the challenge of playing for the Giants, who will enter their third season in 2014, would be something he would be excited about.
"They're a young club with a lot of exciting young players," he said.
"I said at the start I believed I still had a lot of good footy to give and I still really want to get out there and compete.
"Until I have the clubs saying they don't want me, I'll still keep looking."
Twitter: @AFL_JenPhelan
