CPI-M General Secretary Sitaram Yechury on Friday expressed dismay over the government not suggesting a name for presidential candidate and said the question of cooperation will arise only when the ruling dispensation comes out with a name.

Yechury's remarks came after senior Union Ministers Rajnath Singh and M. Venkaiah Naidu, who are part of the three-member committee constituted by Bharatiya Janataa Party President Amit Shah, met him at the CPI-M headquarters here.

"We had expected that they would suggest some name on which we could have seriously considered. Unfortunately, they did not come forward with any name," Yechury told reporters.

Stressing that support can be given to a particular individual who can uphold the Constitution, Yechury said, "We would have certainly thought about such a person, but they did not suggest any name. So, there is nothing to think about when they did not suggest any name."

The senior communist leader said the government side has assured they would come up with a name after three-four days and "sought our support".

"They (BJP leaders) said the government wants our cooperation. There should be a base for that cooperation. We will think about it when they suggest a name. The two ministers had come on behalf of the government without any name," Yechury said.

On speculation doing the round that the Left parties want former West Bengal Governor Gopal Krishna Gandhi as the opposition nominee, he said, "They (government) know. The names that we are discussing are in public domain."

In a dig at Naidu, Yechury said that in the last general elections, the opposition had got the highest vote share and therefore the mandate of the people is with the opposition.

"In the last Lok Sabha polls, the BJP got 31 per cent vote share and with all the NDA parties it was 39 per cent, while the opposition got 61 per cent vote share. So the country's mandate is with opposition's candidate," Yechury said.

On Tuesday, Naidu had said that the presidential candidate will be decided in the true spirit of democracy — "going by the mandate of the people — and the mandate of people is for the government".