According to The Guardian, employees on the long-running BBC One show were informed of the plans this morning by BBC director of news Helen Boaden.
BBC sources claim that there is enough spare capacity at the new BBC North headquarters to accommodate the around 100-strong BBC Breakfast team.
The morning news programme, which is simulcast on the BBC News Channel, features a team of regular presenters, including Bill Turnbull, Sian Williams and Susanna Reid.
Around 2,300 BBC staff positions are due to make the move from London to the new Salford base, including the corporation's sport, children's, learning and future media and technology departments, along with parts of BBC Radio 5 Live.
Some of the people who have been asked to move to BBC North have requested redeployment within the BBC or taken voluntary redundancy.
However, around half of the full-time employees in positions flagged for relocation have already agreed to make the move from London.
The relocation of BBC Breakfast is among a number of proposals being discussed by the corporation's management, but it is now thought to have moved higher up the priority list.
A source close to the programme said: "People are in shock. They had no idea this was on the agenda."
A BBC spokesman said: "The BBC has always been clear it wants to move more output to Salford. But as to who will go, a decision has not been made, [and] a number of options are being considered."