If voted to power, the Congress and its allies will sit together and decide who will be chief minister.
"No one person can claim that he or she shall be chief minister... There is a broad, strong secular alliance (and the leader will be elected) in a democratic spirit," Congress spokesperson Abhishek Singhvi said in New Delhi on Friday.
The statement comes ahead of Congress president Sonia Gandhi's campaign for the second phase of the assembly election in Bihar.
When told that his statement was at variance with that of Rashtriya Janata Dal Chief Lalu Prasad, who has been insisting that there was "no vacancy" for the post and the poll was only to renew the term of his wife and Chief Minister Rabri Devi, he said, "I have said what I have to say. I speak for Congress party and not for anybody else."