The corporation plans to give the project a new name, possibly the BBC North Project, switching the focus away from the city itself.
"Putting the Manchester label in the early strategy was helpful because people knew where we were going. But the benefits stretch much wider than Manchester," said project director Mark Thomas.
Questionnaires have been sent to the 1,800 staff likely to be affected, asking what their concerns are over the move, and results are expected to be given to staff over the next few weeks.
"Your first reaction to something like this is do I want to go or not, and why are we doing this?" said Thomas.
"With the timeline we've got and the number of people who are indicating that they're interested in moving, I don't think we're going to have a problem."
The relaunch comes after the departure of one of the key architects of the Manchester move, director of sport Peter Salmon, who left this week to become chief executive of indie TV Corporation.
He had co-chaired the Manchester project with director of nations and regions Pat Loughrey, and was tipped to become a "director general of the north".
Having an enthusiastic figurehead there is seen as important to the success of the move.
A BBC source said: "The assumption is that there's going to be a some sort of central figure, not just to manage Manchester, but to bring together the departments."