'I'm sure we will find someone good for the role,' the spokesman said and confirmed that programme makers were in talks with Casanova actor Tennant.
No firm decisions had been made but Billie Piper will reappear as Rose.
Announcing his departure, Eccleston said: 'The audience's response to the new Doctor Who has been incredible. I'm really proud to be part of it.' Eccleston had previously been approached to play Doctor Who in a film version eight years ago. He turned it down because did not want to be associated so early in his career with a 'brand name' that could rule him out of other parts.
The BBC announced it was planning a Doctor Who Christmas special.
Jane Tranter, head of drama commissioning, said: 'I want to make Doctor Who again, but there is a mischievous element to it, in that you can keep regenerating (the Doctor).'
The programme, which first appeared in 1963 and attracted huge audiences, was scrapped 16 years ago.