McGurk, who was editor at The Scotsman before joining the Telegraph Group, has not left the company but it is unclear whether his future will be at the Telegraph Group.
He was tasked with overseeing cost-saving exercises at the group's Sunday and daily editions, but it is understood he encountered problems among staff and management over a number of issues, including his calls for a job cull at the Telegraph's foreign desk.
There has been no statement from the Telegraph Group.
Prior to joining the Telegraph Group, McGurk became editor of The Scotsman in October 2004, the title's seventh editor in five years.
He was at The Scotsman for 10 years in total before announcing his departure in June this year, and was replaced by Mike Gilson, former editor of The News in Portsmouth.
Meanwhile, senior management at the Telegraph Group have said they are "surprised" at the result of the recently called three-day strike action, which will take place from November 14 to 16, over proposed job cuts.
A statement read: "At this time of massive investment in the future of the Telegraph Media Group and the extensive changes occurring throughout our industry, the union's decision is surprising."
Of the 276 NUJ members at the Telegraph Group, 85 voted in favour of strike action, with 29 against.
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