CPI-M today held its two-day state council to discuss the issue while CPI's state executive is meeting here tomorrow in which the issue is likely to be discussed, party sources said.
The development comes in the wake of Jayalalithaa-led AIADMK's insistence on allotting only one seat each to the two Left parties against their demand for three seats each.
CPI (M) state secretary G Ramakrishnan said several rounds of seat-sharing talks have been held with AIADMK leaders "but there has been no improvement."
AIADMK is yet to react to the latest development.
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On February 24, Jayalalithaa had announced her party's candidates for all 40 Lok Sabha seats--39 in Tamil Nadu and one in Puduchery, saying her nominees will withdraw from the seats that would be allocated to the Left parties.
The Chief Minister has made a pitch to win all 40 seats so that her party could have a greater say in the formation of next government at the Centre.