The 32-year-old defender has been linked with a move away from west London this summer, and might be tempted by the huge tax-free salary he stands to earn in France.
Terry will be offered a two-year deal with wages of £150,000-a-week, which amounts to around £7.8million in total, and with only one-year remaining on his Chelsea contract, could be open to a transfer.
A move to the newly-promoted Ligue 1 side would also see Terry reunited with former Chelsea manager Claudio Ranieri, who is determined to lure the former England international to the Stade Louis II.
Standing in the way of Ranieri and Monaco owner Dmitry Rybolovlev's astonishing recruitment drive is Jose Mourinho, who was yesterday confirmed as the new Chelsea manager, returning for a second spell in charge at Stamford Bridge.
The former Real Madrid boss is set to make a decision on Terry's Chelsea future as one of his first tasks, determining whether or not to keep the centre-back.
Having served the club for almost 15 years, Terry will obviously be keen to stay, but as he finds himself increasingly marginalised, the opportunity for more regular first-team football will also be an attractive proposition.