The 36-year-old has found first team opportunities limited under new manager Antonio Conte this season and has not started a Premier League game since the 2-2 draw against Swansea back in September.
Chelsea have not offered their captain a deal to remain at the club beyond the current season and a number of sides have shown an interest in taking the former England captain on loan until the end of the season.
Bournemouth, Swansea, West Ham, Crystal Palace and Leicester are among a number of clubs interested in Terry, according to the 'Daily Mail', but the defender is keen to stay at Stamford Bridge.
It is thought that Terry would rather stay in west London, rather than play for another team for the rest of the season, and help the Blues challenge for the Premier League title and the FA Cup.
Terry is expected to be offered a non-playing role at Chelsea beyond the current season, but should he decide to continue his playing career, it's almost certain that he would have to look elsewhere, the MLS being a potential option.