Mr Bansal was not available for comment.
His nephew, Vijay Singla, was arrested in Chandigarh, where he lives, for accepting Rs 90 lakh in cash from a man named Manjunath who was the middleman for Mahesh Kumar, who was arrested in Mumbai.
Mr Kumar was recently promoted and made a member of the top governing body of the railways.
However, he allegedly wanted to "buy" a different post.
The arrests followed a tip-off after which the CBI tracked Mr Kumar's movements and phone calls. They allegedly caught the minister's nephew as he was accepting the bribe.
Mr Bansal was made Railways Minister a few months ago after Mamata Banerjee pulled her Trinamool Congress out of the ruling coalition.
A series of high-profile scams have led to the opposition declaring this government "the most corrupt since independence."
The controversy around Mr Bansal will embarrass the government further at a time when national elections are just months away.