CPM general secretary Sitaram Yechury said that the non-NDA parties will take the decision "keeping in mind the country's history that the ruling and opposition parties contested the polls on all occasion except once".
Neelam Sanjiva Reddy was the only President who was elected unopposed. He had served between 1977 and 1982.
"It was their (NDA's) proposal that they will get back to the opposition after zeroing on a candidate. They did not come back to the opposition and announced the candidate," Mr Yechury told reporters in New Delhi.
"So, we said the opposition will meet and take a decision on June 22. All the opposition parties will try to reach a common decision," he added.
The BJP today named Dalit leader and Bihar Governor Ram Nath Kovind, who has been associated with the party, as the NDA nominee for the top constitutional post.