At least four members spoke on the proposal, forwarded by the CPI(M)'s West Bengal unit, after it was mooted in the morning session of the three-day meeting. The leader added that a decision may be made during the second session of the meeting today itself.
According to a CPI(M) norm, none of its leaders can have more than two terms in the upper House. Yechury himself has already stated that he will stick to the norm being party's general secretary.
"So, the central committee will have to take a decision before that deadline. The issue came up for discussion in the morning session. More discussion is expected on the proposal in the second half.
"Voting will be held on the proposal, if need be. We hope the decision is made today itself," the leader said.
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He said the 91-member central committee stands divided on the proposal, particularly the Kerala unit is opposed to the idea of sending Yechury to the upper House again and that too with the support of Congress.
The Congress has been the arch rival of the CPI(M)-led Left Democratic Front in the southern state.
The West Bengal unit of the party had in June this year recommended another term for Yechury. This was after the central leadership of Congress reportedly offered its support to Yechury, considered as one of the effective opposition voices, to get him re-elected to the Rajya Sabha from West Bengal.
The Left Front has 32 MLAs, including 26 of the CPI(M), in the West Bengal assembly. The numbers are not enough to send Yechury or any other Left leader to the Rajya Sabha again.
However, with the support of Congress' 44 MLAs, Yechury could easily be re-elected to the upper House, the leader said.