The e-mail, which McCann strenuously refutes, states that the agency's digital production arm, Chrome, "plans to borrow directors from member companies".
In a strongly worded statement to the APA, a McCann spokesman said: "We take issue with the recent APA e-mail to member companies.We have no intention of borrowing directors from production companies.
"Moreover, we are well aware of the talent and resources available to us from APA production companies and their directors, and will continue to recognise this."
The row is understood to have erupted following McCann's recent appointment of Stephen Worley to the new position of head of broadcast.