"There is a strong possibility of the two leaders meeting," a senior Sena leader told PTI.
Thackeray recently broke ranks with the BJP-led National Democratic Alliance on the presidential issue, saying his party would vote for Mukherjee in the Presidential poll slated for July 19.
Pranab Mukherjee (R) likely to meet Shiv Sena chief Bal Thackeray (L)
Having declared his party's support for Mukherjee in the Presidential poll, Thackeray recently described him as a 'super power' in the UPA government and said the Opposition should be happy that with his election the government would become a 'lame duck'.
"Mukherjee is a super power in the Manmohan Singh government and because of his going in the Rashtrapati Bhawan, the government is going to become a lame duck. That is why Opposition parties should be the most happy ones to see that he is going to Rashtrapati Bhawan," Thackeray had said.
In the 2007 poll also, Thackeray had supported the UPA choice Pratibha Patil, breaking ranks with NDA on the issue of her being a Maharashtrian.
On reports that Union Agriculture Minister and NCP chief Sharad Pawar, an old friend of Thackeray, would accompany Mukherjee to the meeting, NCP sources said, "nothing is impossible".
In 2007, the then chief minister Vilasrao Deshmukh (Congress) and deputy chief minister, R R Patil (NCP) had visited Thackeray's home in suburban Bandra to thank him for supporting Patil.
During his visit to the city on July 13, Mukherjee is also expected to meet UPA MPs and legislators from the state.