"We can not probe private deals without specific allegations or quid pro quo," Chidambaram said while replying to questions at the annual Economic Editors' Conference here.
Chidambaram said the company and the individual concerned had made statements and the government cannot investigate the matter on allegations based on "implied quid pro quo".
"Transactions between two private individuals cannot be questioned on the basis of some imputed or implied act of corruption. Nobody has alleged any quid pro quo or corruption," he said.
India Against Corruption activists Arvind Kejriwal Prashant Bhushan had alleged last week that companies owned by Vadra, son-in-law of Congress president Sonia Gandhi, had bought properties and land from realty major DLF worth beyond their capital base.
They also alleged undue favours to Vadra's companies from the governments of Delhi, Haryana and Rajasthan -- charges that were denied by Vadra, DLF, the respective state governments and the Congress party.
The finance minister said the government has no facts to establish whether the allegations against DLF and Vadra were right or wrong.
"I am not aware of the rightness or wrongness of the allegations. All I can say at this moment is that this allegation pertains to transactions between two private entrepreneurs," he said.