The Stones kicked off the Australian leg of their latest tour in Adelaide last night and will finish in Brisbane on November 18.
They are expected to arrive in New Zealand on the day of the music awards.
The veteran rockers would be in good company. Kiwi superstar Lorde will attend the party, but is not performing, after being nominated in five categories.
"This is not the rubber chicken awards and we are very rock and roll," McKay said.
"In the past we have had international artists like Mumford & Sons and Ronan Keating present awards while here on tour.
"To have the Rolling Stones on board in any capacity would be fantastic.
"We are not a stuffy bunch and would treat the band to some good old Kiwi hospitality, which I am sure they would enjoy."
The Rolling Stones were forced to reschedule their Auckland concert after the suicide of Jagger's girlfriend L'Wren Scott in March.