The party's Politburo and the Central Committee, which met in Delhi last week, had left the delicate matter to the state unit to decide, apparently factoring in the factional trends that have been troubling the state unit for long.
According to CPI-M sources here, the party's state secretariat would discuss the issue first and form its opinion, which would be presented to the state committee later in the day for taking the final decision.
CPI(M) General Secretary Prakash Karat and Politburo member S Ramachandran Pillai are attending the meetings representing the central leadership.
It was almost certain until a couple of months ago that 87-year-old Achuthanandan would not be put up again, but the sudden upperhand gained by issues like alleged corruption and scams have boosted his popular appeal.
This has made even his foes in the party to have a rethinking on his utility in the grim battle with the Congress-led UDF, which has performed quite well in the last Lok Sabha and civic polls.
Achuthanandan himself has made it clear he is prepared to lead LDF once again if the party entrusted him with the task.