The report comes days after Telefónica O2 announced plans to outsource the majority of its customer service facility (Voice) to Capita, resulting in the transfer of 3,000 employees and 600 redundancies.
Prospect National Secretary Ben Marshall said: "The Telegraph scenario would mean the loss of many more jobs than originally anticipated, including those of managers and professionals represented by Prospect.
"We opposed in principle the plans to outsource these call centres to Capita. However, we entered into talks with both companies in good faith, in order to seek the best outcome for our members and ensure any redundancies were voluntary. Now it seems there has been a breach of trust, if Capita was already secretly planning to close at least two sites at the end of two years.
"We are seeking urgent new talks to clarify Capita's genuine intentions beyond the two years for which a certain element of job security was agreed."
The documents seen by the Telegraph suggest Capita plans to keep only around 1,370 of the 3,700 O2 staff being transferred, with a possibility of redeploying a further 500 within Capita. Instead it plans to outsource work to South Africa and India.
Marshall said: "The dismay of loyal, hardworking staff was compounded by the fact that the company plans to begin the transfer on July 1 – only 40 days after consultations began, in line with new government legislation."
The decision affects staff at four Telefónica sites – Bury, Glasgow, Leeds and Preston Brook (near Warrington).