Prakash Karat, Sitaram Yechury and S Ramachandran Pillai (CPI-M), AB Bardhan, Sudhakar Reddy and D Raja (CPI), Debabrata Biswas and G Deverajan (Forward Bloc) and TJ Chandrachoodan (RSP) will attend the meeting, Left sources said.
Left parties account for around 51,000 vote value in the electoral college of 10.98 lakh vote value.
Prior to the meeting of Left parties, the CPI(M) Polit Bureau is also meeting in the capital where the issue of Presidential poll will be discussed among other subjects.
The Left parties have maintained a suspense on the issue of support to the UPA nominee, saying they were not bound to back the ruling coalition's candidate.
"We are not bound, we are not part of the alliance of Congress and UPA that we have to support anybody they propose," CPI(M) General Secretary Prakash Karat has said.
The CPI(M) had earlier decided to consult secular and Left parties before finalising a stand on supporting a Presidential candidate.
Top leadership of UPA has already spoken to Karat and Bardhan seeking their support for Mukherjee.
The Presidential poll, slated next month, was also discussed in the recent CPI (M) Central Committee meeting, which authorised the Polit Bureau to formulate the party's strategy on the election after discussing the issue with other Left and like-minded secular parties.