Bardhan said the ruling United Progressive Alliance headed by the Congress party should first declare its candidate, though it has given its preferences.
"First of all, the biggest party, the ruling party, which has the maximum votes, should point who its candidates are. After that we will decide. We, the left, are meeting on 21st (June)," he said.
Bardhan further said that he has so far discussed the issue with Orissa Chief Minister Naveen Patnaik, Tamil Nadu Chief Minister J Jayalalithaa, Nationalist Congress Party chief Sharad Pawar and Telugu Desam Party chief N. Chandrababu Naidu.
"Pranab Mukherjee has at least not talked to us. The only persons who have talked to me on the presidential elections are Naveen Patnaik, Jayalalithaa, Sharad Pawar and Chandrababu Naidu," added Bardhan.
Bharatiya Janata Party veteran LK Advani, who is the National Democratic Alliance's working chairman, had met Tamil Nadu Chief Minister J Jayalalithaa in Chennai following which the two leaders decided to coordinate their efforts for the presidential election.
"We discussed the presidential elections. No decision by the NDA till the Congress announces its candidate," Advani told media after his meeting with Jayalalithaa on Thursday.
BJP leader Ananth Kumar had earlier said the NDA would decide on the presidential candidate after the Congress party came out with a name.
Trinamool Congress chief Mamata Banerjee and Samajwadi Party chief Mulayam Singh had on Wednesday evening announced the names of Manmohan Singh, APJ Abdul Kalam and Somnath Chatterjee as their choices for the July 19 presidential poll. The two leaders also rejected the names of Finance Minister Pranab Mukherjee and Vice President Mohammad Hamid Ansari as suggested by UPA chairperson Sonia Gandhi.
The Congress party, however, ruled out sparing Manmohan Singh for the presidential race, as it rejected the three names proposed by the two allies, sending signals that it was not in a mood to bow before them.
"Manmohan Singh will stay prime minister till 2014. We cannot afford to spare Manmohan Singh," said Congress spokesperson Janardhan Dwivedi.
Dwivedi also said that the names of former Lok Sabha Speaker Somnath Chatterjee and former President APJ Abdul Kalam as proposed by Mamata and Mulayam were not acceptable to the Congress.
The latest developments appear to be a major blow for the ruling Congress party, as both Mamata and Mulayam have rejected the names of Mukherjee and Ansari.
The Trinamool Congress, with 19 members in the Lok Sabha, is the largest constituent of UPA after the Congress. On the other hand, the Samajwadi Party, which has 22 members in the Lok Sabha, is an outside supporter of the ruling alliance.
President Pratibha Devisingh Patil's term ends on July 24.
