Green's place as number one is under threat after the Hoops pulled off a major coup in signing Brazilian international Julio Cesar from Inter Milan.
Allardyce expects that Green will use his experience to deal with the situation.
He said: "He's a very experienced goalkeeper, an England international so I don't think he'll worry too much about the competition from Cesar.
"Cesar won't be ready for the Premier League. They'll probably play him because of the size of the name but he won't have seen anything like when it comes in and at him here.
"I know he's been at a top club for many, many years but this league is different to what he's used to playing in and that takes some adjusting to. Rob's proven he's one of the best goalkeepers in the Premier League over the last nine or 10 years."
QPR boss Mark Hughes could hand Cesar his debut away to champions Manchester City on Saturday, September 1.