"Congress will like to know what allegation is Rajnathji and his son facing which are being denied," Congress leader Ajay Maken said.
"We also want to ask who put these allegations on the home minister, since the Congress has not done so," he said.
Gossip in the corridors of power says that the home minister's son Pankaj Singh got a dressing down from Prime Minister Narendra Modi in Rajnath Singh's presence over some misconduct.
Later, it was said that Rajnath Singh sought a ticket for Pankaj Singh for the Uttar Pradesh assembly by-elections but was denied it even though he was being seen as a frontrunner for the Noida seat.
Rajnath Singh, the Prime Minister's Office, and BJP president Amit Shah, all denied the reports, calling it malicious and baseless.
Janata Dal-United (JD-U) chief Sharad Yadav, also, said the allegations against Rajnath Singh cannot be true.
"He is a clean and honest politician. These allegations cannot be true, they are baseless," said Yadav.