Green is reaching the twilight of his career, at the age of 35, but that has apparently done little to put the newly-crowned Premier League champions off his services.
The Blues feel that he could offer good back-up for Thibaut Courtois and would be a shrewd value for money option as cover in an important area.
Green has been one of the R's standout players this season and still seems to have something to offer a Premier League side.
If he does move to Stamford Bridge, he will replace Petr Cech as the side's number two, with the Czech Republic international said to be on the verge of leaving – per the Independent.
Green is never likely to displace Courtois, but he would help Chelsea to fill their quota of English players in the Champions League and is a reliable option, should he be called upon.
QPR's relegation to the Championship means that even if Green doesn't leave to join Chelsea, he is likely to move on somewhere this summer.