There was no official word from either Mukherjee or Narayanaswamy on what transpired at the nearly 15-minute meeting held at Mukherjee's Talkatora Road residence.
Narayanaswamy did not speak to mediapersons present outside Mukherjee's house.
Earlier in the day, Congress chief Sonia Gandhi named Mukherjee as her party's first choice for Presidential poll but Trinamool Congress supremo Mamata Banerjee and SP chief Mulayam Singh Yadav came up with the names of former President A P J Abdul Kalam, Prime Minister Manmohan Singh and former Lok Sabha Speaker Somnath Chatterjee as their candidates for President's post.