Rooney skippered his country in a competitive fixture for the first time in Friday night's 5-0 win over San Marino in a World Cup qualifier at Wembley.
The Manchester United star netted twice to become England's fifth highest ever goalscorer with 31 after moving past Nat Lofthouse, Tom Finney and Alan Shearer.
It was a proud night for Rooney in wearing the armband and he hopes he can become a successor to Steven Gerrard when he hangs up his boots.
He said: "As a young player, your dream is to play for England and once you do actually play, the next step is to try and captain your country.
"I've done it now, it was a great honour and a great feeling, and hopefully one day in the future it can be full-time.
"But I also want to help England to be successful. To be successful is a dream, not just myself but everyone in the dressing room.
"Can I hold a trophy up (as captain)? I hope so. It's a long way away. But that's the stuff of fairytales."
Only record holder Bobby Charlton (49) Gary Lineker (48), Jimmy Greaves (44) and Michael Owen (40) are now ahead of Rooney in terms of goals for England.
He said: "It is a great feeling for me to be in the top five and to overtake some great players as well.
"I'm still only 26 with hopefully a lot more years of international football to come and hopefully I can get more goals."
Rooney accepts it will not be a disaster if England share the spoils in Tuesday's testing encounter with Poland in Warsaw although he insists they will be striving for a victory.
He said: "We have to move on from the San Marino game and the victory and we know it will be a tough game on Tuesday.
"I think if we play with the enthusiasm, belief and determination we had against San Marino, then we will be fine.
"It will be tough but we will going there confident and hopefully we can get a victory.
"Nowadays there is no easy game in international football and sometimes a draw can be the point that takes you through the group.
"We want to go and try and get the three points but it may be we have to take a point there.
"You never know, it might be a good point but we will be trying to get the three points."
Rooney is aware of the threat that will be posed by Polish striker Robert Lewandowski who impressed him when recently in action for Borussia Dortmund against Manchester City in the Champions League.
But Rooney has faith in England keeper Joe Hart whom he claimed was the best keeper in the world after his performance for City in a 1-1 draw with Dortmund.
Rooney said: "Lewandowski played well in that game. He had the runners either side of him and they counter-attacked very well.
"That is something we have to be aware of because we know Poland are a good counter-attacking team. We will have to deal with that.
"But, as long as Joe plays well, I'll be happy. He is a fantastic keeper and he is certainly the best to come out of England for a long time.
"He's got 15 years ahead of him. The future is bright for him, that's for sure."