Rooney missed England’s openin two games of the Euro 2012 due to suspension.
He said: “We’re good enough to win it.
“I know obviously everyone doesn’t want us to build up expectations but I firmly believe that we’ve got the players to do it.
“You need a bit of luck as well but we’ve got a good opportunity.
“We’ve always believed. A country like ours needs to be in there with a shout of winning major tournaments and I firmly believe that.
“We’ve got the squad, we’re more organised than we have been as long as I’ve been in the squad and we are hard to beat.
“If we keep doing that and keep working there’s no reason we can’t go really far and be in with a shout of winning it.”
The Three Lions face one of Spain, Croatia or Italy in the last eight if they make it through.
“You have to play the best teams if you want to win tournaments – and how much of a boost would it be for us if we did play them and beat them,” he said.
“How much confidence would that give us?
“You have to play those teams to win tournaments whether it’s quarter-finals, semis or the final. We just have to cope with that.”
