But the CPI(M) did not agree with Basu's description of the offer, a chance that rarely comes the Communist's way in India.
Just after the 1996 elections produced a hung verdict in which the Congress could not come back to power and the BJP failed to prove its majority, the non-Congress stalwarts sat together in Tamil Nadu House to chose their Prime Ministerial candidate.
It was the late V P Singh, who himself had turned down the offer first, suggested that Basu should be made the Prime Minister of the United Front government.
The proposal was taken to CPI(M) by the ever-pragmatic practitioner of politics late Harkishen Singh Surjeet, the then CPI(M) General Secretary.
The Polit Bureau met and riven by differences it forwarded the issue to the powerful Central Committee after a voting.The CC declined the offer saying the party was still not in a position to dictate its policies and would not be able to get them implemented by a coalition government.
When Surjeet conveyed this to UF leaders, V P Singh again suggested that the CPI(M) CC should be asked to reconsider the decision.
From Tamil Nadu House, Surjeet called Prakash Karat to tell leaders to stay back in the capital for an emergency meeting. But the CC again turned down the offer politely.
After Basu, the names of late G K Moopanar and H D Deve Gowda, then Karnataka Chief Minister, came up.
After initial round of discussions with coalition leaders including DMK chief M Karunanidhi over issues like administrative experience, Gowda's name prevailed.But it was Basu who suggested Gowda for the top post citing his experience as a minister first and Chief Minister later of Karnataka.
There was some feeble attempt by some to prop up the name of late Ramakrishna Hegde but it fell by the wayside.
When Basu suggested his name, Gowda said it was for his party Janata Dal to decide on the issue. Bihar Chief Minister Lalu Prasad, who was also JD president, immediately latched on to the proposal and said his party was ready.
The rest is now history.
Gowda went to the hospital in Kolkata last week to pay his "gratitude" to the ailing Basu and recalled the role played by the Marxist leader to make him the Prime Minister.
Years later when asked about his description of the CPI(M) decision as a "historic blunder", Basu said, "yes, I still think that it was a historic blunder because such an opportunity does not come. History does not give such an opportunity."
Basu had said he was offered this post by leaders who knew that he was a Marxist and a Communist as they had no other Prime Minister in view.