The Sun says he wants to use Jose Mourinhoâ€™s Chelsea return to help him land a new three-year deal.
The Blues skipper has been encouraged by the Special Oneâ€™s comments about retaining the soul of the club.
He believes the time is right to start talks on a contract to keep him at Stamford Bridge until 2016.
Terry, 32, has 12 months left on his Â£160,000-a-week deal and has yet to open talks to reach a new agreement.
But he is likely to be frustrated in his hopes â€” even Mourinhoâ€™s return is unlikely to reverse Chelseaâ€™s policy of offering only a 12-month deal to any player past his 30th birthday.