The 33-year-old former England international central defender has again been a key part of Blues boss Jose Mourinho's first-team plans since the Portuguese tactician returned to the club from Real Madrid in the summer and he has not missed any Premier League action to date.
As a result, Terry was hopeful of being handed a new three-year contract at the end of the season as he looks to finish his career with the west Londoners.
However, the Blues have other plans and do not appear keen to offer the veteran stopper three more years, but they will put a 12-month deal on the table and then no doubt review the situation on a seasonal basis.
Frank Lampard was in a similar situation last year and eventually penned a new contract to stay put when he looked set to depart for pastures new. But tabloid reports are claiming Terry is frustrated by the whole situation and will look for a better deal elsewhere in the summer.