Reports from the BBC suggest Chelsea want Green as back-up to Thibaut Courtois, with Petr Cech expected to leave Stamford Bridge for regular football this summer.
But the London Evening Standard understands that QPR manager Chris Ramsey has urged Green to ignore the allure of joining the Premier League champions to remain their first-choice goalkeeper and help them secure immediate promotion to England's top flight.
Green has one year remaining on his contract and was one of QPR's best performers this season, although you could argue that wasn't difficult.
The 35-year-old has been promoted to the Premier League with every club he has represented. Norwich won the First Division in 2004, West Ham United reached the Championship play-offs in 2012 and QPR did the same in 2014.
Now, in 2016, QPR boss Ramsey will hope to achieve that and has previously stated on Sky Sports that in order to achieve immediate promotion it is vital that his squad start next season on a more stable footing if they're to move forward and regain Premier League status.