According to an NDTV report, the two were likely to make the offer at a meeting of the Congress Working Committee on Monday, although they added that the move was largely a symbolic one as the party would not accept it.
The Congress has been decimated in this election, winning just 44 seats
"Sources say emotional speeches will set the tone for deep introspection on the Congress' spectacular rout. India's oldest party was reduced to double digits in Parliament and failed to win a single seat in 10 states, as a long and grueling campaign by Rahul Gandhi failed to stop the tide of public anger", the NDTV report said.
The two top leaders took the moral responsibility following the party's decimation in the recently concluded Lok Sabha election in which it could manage just 44 seats, its worst performance over.
Meanwhile, Prime Minister Manmohan Singh met President Pranab Mukherjee on Saturday to submit his resignation.