Roy Keane was keen on bringing Hunt to Wearside back in 2007-08 but a bid was rejected.
"When I was playing for Reading, my agent told me that Roy wanted to sign me for Sunderland," Hunt told the Off The Ball sports breakfast show.
"There were about 10 days to go in the window, but I had a loyalty to Steve Coppell at the time that meant I would never put in a transfer request to go because he'd always been good to me.
"To be fair to Roy, I've had loads of managers ring me and tell me they're going to bid for me before not doing it.
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"Am I allowed say he phoned me? He made contact, whatever you want to say legally, and bid for me, but Reading turned down £8.5 million for me.
"I was always grateful to Roy for doing that, and the fact that I could grab Reading by the balls and got my new contract after that.
"I said I wanted to go to Sunderland at the time, but Roy signed someone else in my position in the end - Andy Reid I think - so that's football."
Hunt, who has 39 international caps for the Republic of Ireland, spent four years at Reading and the winger made more than 150 appearances for the club.