Green has slipped out of favour at Loftus Road since Jimmy Floyd Hasselbaink took charge, and he was left out of the R’s match day squad against Rotherham United on Saturday.
Alex Smithies and Joe Lumley both now appear to be ahead of Green in the pecking order for places, but Hasselbaink is said to be not entirely convinced by any of his current stoppers.
As a result, QPR are hoping to sign Johnstone from United at the end of January.
Rangers cannot currently pursue a deal as the impressive young 'keeper is on loan at Preston North End, but they allegedly intend to make a bid once his temporary spell at Deepdale comes to an end.
United are looking for a £1 million fee for the 22-year-old, and QPR are reportedly prepared to match that figure.
They could also let Green go in the coming weeks, with both Watford and Bournemouth said to be interested by The Sun.