Andrew Fisher, head of policy and the author of the party’s last manifesto, is said to have walked out last Saturday.
The Sunday Times reports he denounced Mr Corbyn’s team for their “lack of professionalism, competence and human decency” in a memo seen by the paper.
He also said he was sick of the “blizzard of lies and excuses”, and claimed a “class war” had gripped the upper echelons of the party.
His resignation will be a significant blow to 70-year-old Mr Corbyn, who, it is claimed, may also stand down because he feels under “incredible pressure”.
A Labour source said: “We don’t comment on staffing matters.”
It comes as Corbyn has said he would like to see two deputy leaders of the Labour Party – hours after a bid to scrap the elected position was abandoned.
The Labour leader said one of the deputies should be a woman to reflect the “diversity within our society”.
It came after Tom Watson, who has repeatedly clashed with Mr Corbyn, claimed the civil war at the top of the party had undermined efforts to present itself as an alternative government.
An attempt to oust him by scrapping his elected position was abandoned on the first day of Labour’s conference following an intervention by the party leader.
Mr Corbyn said: “I told the national executive we need to review how the deputy leadership works and have an election process for two deputy leaders in the future which reflects diversity within our society so one would be a woman.
“It was agreed overwhelmingly.”
He added: “Tom is the elected deputy leader of the party and so has an important role to play.
“I work with him and he’s done very well on media reform, online gambling and exposing the way sugar has a deleterious affect on our lives.”