The 28-year-old’s place in Roy Hodgson’s starting line-up for this summer’s World Cup in Brazil has come under scrutiny in the wake of Manchester United's disappointing season.
However, Rooney ended a run of four international matches without a goal by scoring in the 2-2 draw with Ecuador in Miami on Wednesday as part of a good display in an unfamiliar position on the left wing.
In response to the criticism from Scholes, Rooney said: "To be honest, I'm not really interested in what anyone else has got to say.
"I'm interested in what Roy Hodgson and the coaching staff here and the people around me say. People have their opinions but I don't agree with them.
"[Scholes has] been a team-mate but he's been away from the first team for a long time.
"I've seen a lot of you (in the media) saying he's coached me and been around the team but he hasn't. I'm not really going to react. I'm not interested. He's got his opinions so let's leave it at that."
Rooney's position in the national side has also been questioned by former striker Gary Lineker, who suggested the displays of other England players has left the Manchester United man vulnerable.
Lineker pointed to Daniel Sturridge - who scored 24 goals last season and also netted a superb goal in the 3-0 friendly win over Peru last Friday – but Rooney believes he and the Liverpool forward can play together.
"I'm not 100 per cent sure but I think in every game we've played one of us has scored (they have actually scored in five of the last seven games)," Rooney said.
"Daniel's a fantastic player. He can score goals from anywhere like he did at Wembley [against Peru].
"We have trained a lot together so hopefully we can take that form into the tournament."
Rooney has yet to score a goal at a World Cup finals, having gone into each of the last two tournaments carrying an injury, but he says he is fit and ready to lead the line for England in Brazil.
"I've said before I've trained hard, no injuries or recurrence of the groin strain I had at the end of the season," added Rooney.
"I always would have needed game time such as the first game at Wembley and (the Ecuador game). I felt really good, especially in the heat.
"I'm ready to play. I'm sure the manager will have a tough decision but I'm ready. I hope to play on Saturday (against Honduras).
"I can play in different positions. I've proved that over the years. It is down to the manager. It is not about me, it's about the team. If the manager wants to play me up top, in behind, left, right, I'm happy to do that."