The 36-year-old joined the Championship club in the summer.
The former England stopper joined the Whites earlier in the summer after leaving Queens Park Rangers. And while his time at Loftus Road ended in disappointing fashion - as he failed to make a single appearance for the Hoops after New Year's Day - the Yorkshire Evening Post reports that he is expected to be Garry Monk's first-choice after the new United boss expressed a desire to have a man with plenty of experience between the sticks.
And Green has confirmed that he does not intend to simply see out the final years of his career on the periphery of the team.
"I'm looking forward to getting out on the pitch. It's been a while," he told the Yorkshire Evening Post.
"I've not come here not to play. I want to play and I want to play as many games as I can. I want to look back one day and say that I had 10 great years at Norwich, six great years at West Ham, four great years at QPR and X-amount of great years at Leeds.
"I want this to be up there with all of that in terms of longevity and success. It's not like I'm here to sit back, relax and chill. I could have done that by staying in London, sat on the bench somewhere, but I've come here to be part of something - something exciting."
Leeds manager Garry Monk
While the 36-year-old is currently confident of his place in the side, he will know that there are more than enough options for Monk to pick from if he fails to find his best form.
Ross Turnbull has plenty of experience while Bailey Peacock-Farrell is arguably one of the brightest prospects knocking on the first-team door at Thorp Arch currently.
Meanwhile, although Marco Silvestri's days with the club previously appeared to be numbered as he was sent home from a pre-season tour to train with the youngsters, the Yorkshire Evening Post reported that the Italian - who has spent the last two seasons as the club's number one - had worked his way back into Monk's plans after impressing the manager with his attitude.
And although the Yorkshire Evening Post reports that Silvestri is still free to leave if a bid comes in, Monk may feel that if the 25-year-old stays, he may be the perfect replacement if Green is struggling as he will undoubtedly have a point to prove.