A number of high-ranking figures in the commercial department, which is headed by Dave King, are known to be facing redundancy. Several senior journalists are also reportedly heading for the exit.
A source said it was "not a good day" after management told some of the affected individuals on Monday.
There were claims that as many as 100 staff have been warned that their jobs are at risk, but a person close to the company said this figure is inaccurate without giving further details.
Telegraph Media Group declined to comment but, under employment law, a company must launch a consultation if 20 or more employees are being made redundant within 90 days.
All newspaper groups are under financial pressure after a double-digit decline in print advertising this year.
In a separate move, Murdoch MacLennan, the chief executive of Telegraph Media Group, has told staff in a memo that it wanted to introduce "smart working" to "save significantly on rents and rates".
He wrote: "Our office is never full and even on a very busy day a large number of desks are unused.
"With changes in the way we work, and hot-desking for some of those who need to be in the office, we will be able to reduce the size of our footprint at BPR [Buckingham Palace Road, TMG’s office in Victoria]."
MacLennan’s memo, which was first published in The Guardian, said: "I believe that this will allow many of us to have a better work-life balance and I hope you will welcome this modern, employee-friendly approach that is so much in line with the changes in the media world."
Telegraph Media Group is one of the most profitable UK newspaper groups but its last annual accounts showed a 20% fall to £45.7m.