Speaking to reporters after the nearly 30-minute meeting held at the CPI(M) head office here, Yechury reiterated his party's stand that a person with "impeccable secular credentials" should be the next president.
The CPI(M) leader said the opposition parties would wait till the government completed the round of discussions with them to take a call on their nominee for the July 17 presidential election.
The ministers, the sources said, denied the report and told Yechury that the government was yet to finalise any name.
A senior CPI(M) leader wondered if the RSS-BJP combine would let go the opportunity to install a president of their choice since "they are so close to" electing one to the post.
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Yechury said it was required for the government to suggest names for arriving at a consensus.
With no name proposed by the government, Yechury said, the parleys looked "more like a public relation exercise" of meeting opposition parties.
"Since the government is doing it, we welcomed them in our office. Very good, they came here," he said.
"So, a candidate of the opposition is the one who has the mandate. So, the government should also consider that aspect," he said.
Yechury insisted the Centre should also be open to considering the names suggested by the opposition if it made any proposal.
"They said they will get back to us in case they come to some decision on a candidate," Yechury added.
"They said they know the names (of the opposition's probable candidates including Gopal Krishna Gandhi). So, it was expected they (government) will suggest some names. But unfortunately, that has not come," one of the sources said.
The meeting followed Singh and Naidu's meeting with Congress chief Sonia Gandhi earlier in the day.
The two ministers are expected to meet CPI leaders later in the day.
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