Mr Aitchison, 59, announced earlier this year that he will stand down after 16 years in the post.
He will not go until the end of the year and the appointment of a successor will have to be approved by a recruitment panel of councillors.
Mr Aitchison earns 158,553.
John Stevenson, president of the Edinburgh branch of Unison, said: "I won't talk about individual salaries. However, they are talking about bringing savings by taking away senior executives, so there may be more work involved. The chief executive of Edinburgh Council is responsible for a 1 billion budget. If he was a banker, he would be paid a 3m bonus on top of the salary."
Prime Minister David Cameron has said that all appointments of civil servants above the level of 150,000 will need to be approved by the Treasury.
However, the council role is exempt from this because it is a local government position.