“We want a consensus candidate. This is good for the country,” Banerjee told reporters here.
She is also learnt to have backed another term for President Pranab Mukherjee if the government proposes his name, sources said.
Congress Vice President Rahul Gandhi was also present in the meeting.
Banerjee said Sonia Gandhi, who has been holding talks with opposition parties to decide a common candidate, will hold further consultations and she would again meet her in about a week after the process is completed.
Banerjee is expected to meet Delhi Chief Minister Arvind Kejriwal on Wednesday.
The term of President Pranab Mukherjee ends in July. The ruling BJP-led National Democratic Alliance, which has clear edge in the presidential election, has not given any inkling so far on its choice of candidate.
Sonia Gandhi has been contacting leaders opposed to the ruling BJP to evolve a consensus.
She has spoken to Samajwadi Party leader Mulayam Singh Yadav and RJD chief Lalu Prasad and met JD-U leader and Bihar Chief Minister Nitish Kumar, Nationalist Congress Party chief Sharad Pawar, Communist Party of India-Marxist leader Sitaram Yechury and National Conference leader Omar Abdullah.
The Congress chief is also expected to meet Bahujan Samaj Party supremo Mayawati.
Answering queries from media persons, Congress media incharge Randeep Singh Surjewala said the Congress was proud that President Mukherjee came from the pedigree of thought process and an ideology that has been a centre-point of this country since its formation.
He said the names of the candidate would be announced once a consensus is reached.
Among the names doing the rounds as consensus candidates of opposition are of former Governor Gopalkrishna Gandhi and former Lok Sabha Speaker Meira Kumar.