A meeting was held on Wednesday morning involving Dunne, boss Kevin Keegan, club directors and Professional Footballers' Association chief Gordon Taylor.
A statement on the club's official website stated that:
Richard Dunne has accepted the seriousness of his situation having had similar disciplinary problems in the past.
The PFA will now work together with Manchester City Football Club to assist Richard Dunne during this training period and to help him work towards achieving the goals he has set himself.