The Australian ended his eight-year stint with the Toffees during the summer by joining Major League Soccer side New York Red Bulls.
However, the MLS does not run during the English winter, meaning that Cahill will be free to join another club on a loan basis.
With that in mind, the 32-year-old has conceded that he would relish the chance to pull on an Everton shirt once again.
"I know I have a lot more to offer," Cahill told Sky Sports News. "The main thing is that I get to enjoy to MLS but I also get the chance of joining back up in the Premier League and playing in the best league in the world.
"There is no shadow of a doubt, I am eager to come back. Hopefully something can be done [with Everton]. It would be nice but it is not down to me. I have to respect that sometimes the ship has sailed."
Cahill originally joined Everton from Millwall in 2004.