CPI(M) politburo member and Left Front Chairman Biman Bose in a statement said it was nominating Deb for the fifth RS seat from the state.
The announcement came hours after West Bengal Chief Minister and Trinamool Congress (TMC) supremo Mamata Banerjee said her party would support Abhishek Manu Singhvi of the Congress in the RS polls.
Congress is yet to declare the name of Singvi as its candidate from West Bengal.
Banerjee also announced the names of four other TMC candidates for the elections of the Upper House of Parliament.
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