The New York Red Bulls midfielder is "eager" to come back to the Premier League on a temporary basis in between MLS seasons and says he misses playing in Merseyside derbies.
MLS players have often used the North American close season to join European clubs on loan in recent years, with LA Galaxy star Landon Donovan enjoying two spells at Goodison Park.
Cahill has pitched the idea of making a short-term comeback at the club with which he spent eight years in the Premier League.
"I know I have a lot more to offer," Cahill said in an interview with Sky Sports. "The main thing is that I get to enjoy 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 was delighted to see the Toffees emerge once more as a contender for Champions League qualification, with David Moyes' team currently sitting fifth in the table.
The Australian admitted that the match he most missed taking part in is the Merseyside derby.
"I am so happy for Everton and nobody more than the chairman and manager whose rewards are starting to show," he enthused. "The biggest thing I miss is the derby. There are two great teams in one city and when I watch the derby it gives me goosebumps."
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