Cahill was presented by the Red Bulls on Monday after deciding to leave Merseyside for a new challenge in the United States following eight years at Goodison Park. Several US-based players have had loan stints in Europe outside of the MLS season, including David Beckham, Robbie Keane and Landon Donovan, and Cahill was asked if that was something he was considering.
"If something can work and fit to the training regime, because I've committed my future to the Red Bulls, and going on loan might not be the right thing for the football club... But if it works out that I can find the right happy medium to get the fitness and keep training and to play in certain games, then maybe yes," said Cahill
"But I really think in the next three of four months we'll be able to tell closer to the end of the season."
Regarding his move to the MLS, Cahill still has plenty to give and is looking forward to a new chapter in his career.
He also insisted he would not have left Everton for another Barclays Premier League club
"When I had the opportunity to play for the Red Bulls I knew in my heart that if I ever left Everton I would never play for another Premier League team, out of respect for the chairman, the fans and the manger," the 32-year-old said.
"As a footballer I've achieved a hell of a lot in my career but also I feel that this is a big move for me.
"I know a lot of people might think otherwise, but I'm 32 years old, I respect the MLS, I'm coming here at a good age, I'm fit and I'm ready for a new challenge, something that's very special not only for me but also my family.
"I work hard, I give everything and one thing I'm going to do for the Red Bulls is to put my heart into it."