The 36-year-old has spent the last 22 years at Stamford Bridge, with the exception of a brief loan spell at Nottingham Forest in 2000, but has fallen down the pecking order under Antonio Conte this season.
Terry has not started a Premier League game since September and made his first appearance in any competition since November during Sunday's 4-1 FA Cup victory over Peterborough United.
The club captain picked up a red card in that match and will now serve a one-game ban, and with Kurt Zouma returning to fitness and Nathan Ake having been recalled from his loan spell at Bournemouth there is now even more competition for defensive places at Chelsea.
According to The Telegraph, Bournemouth boss Eddie Howe has identified Terry as a potential replacement for Ake, and the possibility of regular first-team football could entice the former England international to temporarily part company with Chelsea.
However, the player is still thought to favour staying at Stamford Bridge in a bid to help them win their fifth Premier League title.