A senior Congress leader, who declined to be identified, said the high command would take a call after the CPI-M's top leadership deliberates on the issue.
The Politburo meeting on Tuesday will be followed by another of the Central Committee on the next two days. Last week, the CPI(M)-led Left Front in the state had formally agreed to discuss the issue of alliance with Congress, if it was approached.
The Congress vice president had told them that party chief Sonia Gandhi will take a decision on the issue soon. His refrain was that in the emerging situation Congress is a "determining factor" in West Bengal.
Before it takes a final call on alliance, Congress would weigh which party in West Bengal could help it check BJP's march in the next Lok Sabha elections.
Congress had contested the last Assembly elections in alliance with Mamata Banerjee's party which dislodged the CPI(M)-led Left Front government after 34 years.
The two parties, however, parted ways in September 2012 after Trinamool Congress walked out of the UPA-II government at the Centre.