Mukherjee, who was named as the first choice by Gandhi in her meeting with Trinamool chief Mamata Banerjee, drove to 10, Janpath and was with her for about 30 minutes.
Senior Congress leaders A K Antony and P Chidambaram also met Sonia Gandhi, besides DMK leader T R Baalu.
The parleys came a day after Banerjee and Samajwadi Party chief Mulayam Singh Yadav rejected Gandhi`s choice of Mukherjee as also of Vice President Hamid Ansari and instead suggested the names of Prime Minister Manmohan Singh, former President A P J Abdul Kalam and former Lok Sabha Speaker Somnath Chatterjee.
Mukherjee did not speak to the media and left with his customary folded-hand greeting. The other Congress leaders were also tightlipped.
Baalu, who emerged last out of the meeting with Gandhi said Sonia Gandhi will be announcing the name of the UPA Presidential candidate anytime later this week.
"Keeping in view of political stature and seniority in public life, my leader Karunanidhi was consulted by Madam last month through Antony. My leader had suggested a name. The name has been communicated by Antony to Madam. Madam at any point of time, will be announcing the decision," Baalu told reporters.
He said the name of the person cannot be divulged as of now and parried questions on whether the candidate is among the five persons whose names have been made public.
"Madam will announce it shortly. Not today... At any point within this week," he said.
When asked if DMK was fine with Mukherjee`s candidature, he said, "it is between the two higher ups. My leader has communicated the matter long back. We stand by it."