The 45-year-old said there is "so much still to be done" at the Scottish Premiership club as he passed up on the chance to return to England
Derek McInnes has rejected Sunderland after holding talks over the vacant manager's role.
Aberdeen confirmed on Wednesday that they had given the Black Cats permission to speak to the manager and assistant Tony Docherty as they prepare for life in the Championship after being relegated from the Premier League.
However, the former Rangers player has passed up the chance to succeed David Moyes to continue with the Dons after guiding them to second place in the Scottish Premiership.