The Australian is currently enjoying life in the MLS with the New York Red Bulls, but he revealed that he has always kept in touch with his former boss as well as a number of his old team-mates.
The 33-year-old was signed for the Toffees by Moyes in 2004 and went on to make 226 appearances during his time at Goodison, helping the Merseyside club to achieve Champions League football.
Cahill believes that his former boss is the right man to take over at Old Trafford and hailed the positive impact he had on his career.
Cahill said: "I text to wish him [Moyes] all the best and I got a really nice text back.
"Every day I'm on the phone to Phil Neville and we are always talking about Everton and how much David Moyes means to the club.
"He is probably one of the closest people in football, in a manager's role, that I can turn to for support or anything to do with football."