"They did not come forward with any name. They said that they want our support. Support can be given to a particular individual. We want such a person who can uphold the Constitution. We would have certainly thought about such a person, but they did not suggest any name. So, there is nothing to think when they did not suggest any names," Yechury told ANI.
"They said they will hold consultations and come up with a name after three to four days. After three to four days, nomination will begin. They said the government wants our cooperation. There should be a base for that cooperation. We will think about it when they will suggest a name. The two ministers had come on behalf of the government without any name," he added.
The ministers earlier in the day met Congress chief Sonia Gandhi at her residence to discuss matters related to next month's presidential elections.
Both of them have already spoken to Nationalist Congress Party's (NCP) Praful Patel and Bahujan Samaj Party's (BSP) Satish Mishra.
Naidu yesterday spoke to Nationalist Congress Party (NCP) chief Sharad Pawar and Telugu Desam Party (TDP) chief Chandrababu Naidu over the same.
The TDP chief said his party will stand by Prime Minister Narendra Modi's decision in this regard.
The last date of nomination is 28 June.