His comments come after the Supreme court refused to direct the Centre to transfer the contributions made to the PM CARES Fund for battling the Covid-19 pandemic to the National Disaster Response Fund.
"Was the Fund set up by the central government as concluded by the Ministry of Corporate Affairs? If not, who set up the Fund and in what capacity?" he asked in a series of tweets.
"If the Fund was not set up by the central government, why are the PM and three Ministers serving as Trustees? Who appointed them as Trustees?" the senior Congress leader asked.
"If the Fund is a private established fund, why are donations to the Fund counted against CSR? Will donations to other privately-established funds be also counted against CSR," he tweeted.
The former union minister asked who authorised the Ministry of Corporate Affairs to make a retrospective amendment to the Schedule to the Companies Act inserting the name of PM-CARES Fund in the Schedule.
Chidambaram also asked if the Ministry of Corporate Affairs would insert the names of other privately-established funds in the said Schedule to the Companies Act.
"The retrospective amendment in favour of a privately established fund is obviously an act of favouritism and discriminatory. It will be challenged," he added.
After the apex court's decision on the PM CARES Fund, BJP leader and Union Minister Ravi Shankar Prasad had said on Tuesday that "transparency is writ large in the PM CARES Fund".
Reacting to the judgement, BJP president J P Nadda said it was a "resounding blow to the nefarious designs" of Congress leader Rahul Gandhi and his "band of rent a cause" activists.
"The country very well knows that the orchestrated smear campaign against PM CARES is an attempt by the Congress to wash its sins," he had said.