The 28-year-old Manchester United striker is now captain of his country following the international retirement of Liverpool's Steven Gerrard.
His first task is to fire England to Euro 2016, with a positive start made to qualification, and Roy Hodgson's side will seek a third straight win against Estonia on Sunday.
That outing will see Rooney earn his 99th cap and provide an opportunity to add to his 42-goal haul.
He needs seven more strikes to draw level with Sir Bobby Charlton at the top of the scoring charts and 26 outings to equal Peter Shilton's record haul.
Rooney said of his double target: "I believe 125 is possible. It's 16 or 17 games before the Euros start, so I won't be too far away then and I have at least another two years after that.
"I couldn't imagine that when I made my first appearance for England. At that age, you don't look beyond the next game.
"You are lucky and it is a privilege to play for England.
"I've always said I don't want to stop playing for England after I get 100 caps.
"I want to get many more after that and try to do my best for the team. It's an honour to play for England, which I've said many times.
"Everyone has seen what the likes of Steven Gerrard, Frank Lampard and Ashely Cole have done in recent times.
"They have passed the 100-cap mark and, hopefully, I will play in the next two games and do that, too.
"It will be a proud moment for me. I have no regrets in what I've done.
"I've tried to do everything I can on the football field the best I can and have no regrets with any choices I've made."
Rooney, who will once again skipper the side in Tallinn, added: "Unless told otherwise by the coaches, I will always be available for selection.
"I've never thought about not playing for England.
"That time will come later but, at the moment, it is not even close to entering my mind.
"I love playing for England and I feel I have many more years playing for England."