Cahill was officially unveiled by the Major League Soccer franchise in New York on Monday following his $1.5 million switch from Everton.
And the 32-year-old said his new team will take precedence in the short-term over the desires of Socceroos coach Holger Osieck ahead of the two friendlies.
Australia play Scotland on August 15 before a second friendly against Lebanon on September 6 before their World Cup qualifier with Jordan on September 11.
Cahill said he hadn't ruled himself out of the matches but his availability will be determined by the Red Bulls.
"We'll speak to Holger about the games, but I really need game-time here to put everything into this and to make sure that I'm doing everything right to get fit," he told reporters.
"That's something me and the boss will talk about but at the moment Red Bulls take priority."
Cahill said he'd informed Osieck of his intention to move to the United States but that he wouldn't have changed his mind if the German said the move would affect his hopes of making Australia's 2014 World Cup squad.
"I texted Holger beforehand and told him this was my move," he said.
"I don't think anyone could have changed my mind about this regardless of their thoughts, good or bad."
The likelihood of Australian fans ever seeing Cahill compete in the A-League look slim, with the Sydney-product saying he never contemplated a move back home.
"Moving to the A-League would have been a step backwards and that's no disrespect," he said.
"I want to still play at a high level. There's still another World Cup for me to play in and to qualify for with the Australian team. This is a massive opportunity.
"I didn't speak to any A-League (clubs) and it was never in my plans ... I'm more interested in the grassroots level of football in Australia, not playing there."
Cahill's American journey will begin when he makes his first outing for the Red Bulls against Premier League team Tottenham in a friendly match in New York on Tuesday (Wednesday 0900 AEST).
Cahill is likely to play a half of the fixture against Spurs and says he's looking forward to getting straight into the action.
"I know playing tomorrow night might be a bit quick," he said.
"But I'm here now, I'm feeling fit, I'm feeling good."