"We want a non-Congress nominee for the post of Vice-President," Bardhan, a CPI central secretariat member, told reporters here.
He said the Prime Minister had telephoned him yesterday and also contacted CPI General Secretary Sudhakar Reddy on the vice-presidential election.
On the likelihood of the Left extending support for continuation of Hamid Ansari as Vice-President, Bardhan said "two to three names have cropped up for the post but we have not made any suggestion in this connection.
"We will discuss the issue in the event of Prime Minister and his alliance partners finally declaring the candidature of Ansari," Bardhan who is here to participate in a state-level meeting of CPI, said.
He admitted there were differences among the Left on supporting Pranab Mukherjee for the post of President but said Left parties were together on other issues.