David Mackay had been trying to merge Edinburgh's tram and bus companies, but walked out because of the “mess” involved in combining them, according to The Scotsman.
The paper also suggested that he no longer wanted to be associated with the failing tram project.
The result of an ongoing legal dispute with contractor Bilfinger Berger is expected in December.
But local MSP Shirley Anne Somerville warned against sacking the construction team.
She said: "If David MacKay's resignation reflects the state of negotiations with the contractors then this city could be facing real problems.
"If someone with his experience cannot tough these negotiations out what does it say for the future. Does his departure mean the contractors are winning?
"Sacking contractors without resolving disputes will only cost this city more."