The England international, who is leaving Chelsea this summer, is said to be close to agreeing a spell with the A-League side before moving to newly-franchised MLS team New York City.
Ahead of Melbourne City's trip to a training camp, Munn was asked about the potential arrival of the 36-year-old midfielder.
"As a standard rule we don't comment on any media speculation," FourFourTwo quotes Munn as saying. "But if, since January when CFG (City Football Group) acquired us, if we'd signed every player linked to us we'd have 60 players flying with us tonight.
"For us, we're really happy with how our list is coming together and really looking forward to a couple of weeks pre-season."
The A-League side were previously known as Melbourne Heart before Manchester City's owners took over.