The newspaper quoted sources as saying the parting was 'amicable' and the airline will begin an immediate search for a successor.
The Irish Mail on Sunday also reported that Mr Mannion was set to leave.
A spokeswoman for the airline has declined to comment.
Mr Mannion has fought off two takeover bids from Ryanair since taking over as Chief Executive in 2005.
The airline has said it was unlikely to make a pre-tax profit this year due to stiff competition and recession.
