The former England captain has not played for the country since 2009, but he has refused to ever formally retire.
The England manager told The People: "I am pleased for him going to PSG. But I think he is going there to continue his career in the same way he did at LA, not to revive an England career.
"If he pulls me aside and says, 'I am going to play well in France so keep me in mind'. I will say, 'Fine, David, I would love to do that'. But I am not expecting that to happen.
"I think he will be a part of English football's future but I do not think he is going to Paris to revive his international career."
The 37-year-old has signed a five-month contract with the Ligue 1 side.