The former England captain is a free agent after he left Aston Villa earlier this summer.
He told the Daily Mail: "When we spoke in the summer, it wasn't long after the season and I was still hurting. I loved my time at Aston Villa. I am still devastated that we didn't go up. The manager, players and supporters were incredible with me but I hate losing and I feel there is unfinished business there.
"Steve Bruce is a great man and with the backing of the new owners, Steve will hopefully get the club back into the Premier League.
"Don't get me wrong, if I don't play again I am content with what has been an unbelievable career, but I'm still hungry to go and play if everything around it is right. If it's right for me and my family."
Terry, 37, is a free agent. There are at least four offers on the table, including a Premier League team and clubs from abroad.
"I am in the best condition I have been in for the last eight to 10 years of my career. I've had a brilliant summer, the first time in 20 years I have been able to get away like that with my family during the school holidays. I was away so much last year because I was fully committed to giving everything to Aston Villa, but now I am fully recharged."