The reigning Premier League champions have been tracking the progress of the highly-rated midfielder for some time, and are keen to lure him away from west London.
Hunte has been tipped for a bright future in the game, and Chelsea are hoping to convince the talented teenager that his future will be better served at Stamford Bridge, rather than moving to the Etihad Stadium.
After impressing in a youth-team game against City last weekend, in which the Blues ran out 2-0 winners, Roberto Mancini wants to take a closer look at the 16-year-old with a view to making an offer for his services.
Should the Citizens succeed in poaching Hunte, then they will have to pay Chelsea compensation, with the amount decided by a tribunal if the two clubs can't agree on a fee.
Already capped at England U17 level, the midfielder is set to line up against Crystal Palace this weekend, where City scouts will be watching him in action as they consider their options.