The bench said that the issue raised by Yadav "requires our examination whether the allegation is correct or not" and issued notice to CBI which is the prosecuting agency in the case.
It said, "If CBI says there is no bias then we would dismiss the petition."
The bench granted two weeks time to CBI and the state of Jharkhand to respond on Yadav's petition and posted the matter for hearing on July 23.
Senior advocate Ram Jethmalani, appearing for the RJD supremo, said that there is apprehension of bias as the judge is related to a minister in the government of Nitish Kumar, "who is his (Yadav's) biggest political enemy".
Yadav approached the apex court after the Jharkhand High Court on July 1 dismissed his plea to transfer the case to another special CBI court from that of Special CBI Judge P K Singh.
The case pertains to alleged fraudulent withdrawal of Rs. 37.7 crore from Chaibasa Treasury in the 1990s.