The 32-year-old has been a bit part player for the Blues over the past 18 months and is widely thought to be past his best, having little physical input in the team which he used to boss.
Terry signed a one year extension with the club back in January but a glamorous move to the south of France may be too good to turn down and could be the perfect setting for him to finish his career.
Jose Mourinho is yet to decide if Terry will remain as Chelsea captain due to his lack of game time and the former England defender could be given the chance to lead Monaco.
The mega rich French club have already lured Chelsea target Radamel Falcao in this summer for £50million in a bid to take the Ligue 1 crown from PSG.
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