The 35-year-old's future remains unclear after he said he would leave his boyhood club following the 2015-16 campaign, only for Chelsea to subsequently reveal that they were open to offering him a new deal.
Terry insists his desire is to stay at Stamford Bridge, but he admits that he is willing to look elsewhere if no offer is forthcoming.
"I'm very hopeful," he said. "I've been there 21 years and I'll never kind of give up until it finally happens. But, who knows?
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"I've still got a lot to give, whether that's here [Chelsea] or somewhere else, for sure."
Terry was also full of praise for interim Chelsea manager Guus Hiddink, who has suffered just one loss in 15 games since replacing Jose Mourinho in December.
With that run, Chelsea have moved into 10th in the Premier League – just eight points off fourth spot.
"Guus has been phenomenal since he come in. Not only this time, but last time [in 2009] as well," Terry said.
"We can only focus on that and what he's doing at the moment. But he's doing a fantastic job, as are the players at the moment."