Ramsey was appointed to the top job after the departure of Harry Redknapp and secured QPR???s first away win of the season with a 2-0 victory over Sunderland.
Ramsey is currently contracted until the summer but Green, who has been at QPR since 2012, says he ???wouldn???t be surprised at all??? if Ramsey stayed on long term, providing the right results were achieved.
Speaking to Sky Sports News, the England keeper said: “If he comes in and we get the results that we need and we survive, then there???s no better dress rehearsal, no better audition for it.
???He would focus purely on the here and now but the motivation is there for him as well as everybody else.??The lads are fully behind him and we want to do well for him so, in that respect, why not????
Green described Ramsey???s appointment as having given the team ???a bit of clarity??? and said his coaching style was clear and direct, with the whole club behind his plans to fight off relegation.
He said he looked to Crystal Palace???s turn of fortunes under new manager Alan Pardew as an example. with the first step a result against fellow-relegation battlers Hull on Saturday.
The win at Southampton, however, was a turning point for QPR, a win Green described as giving the squad a ???massive lift???.
???That game was one that we went to full of confidence and we took control of the game from early doors,??? he said.
???It was no great surprise to us when we went in the lead. It was probably a greater surprise when we went two up because we haven???t scored that many goals away from home this season but it was one that we felt was fully deserved.
???It was fantastic because we had some fans travel all the way up there and after the back of how every many defeats it was in a row to then to win like that is a real treat for everyone.???