The TMC also refuted allegations by BJP that Basu was intimidated and forced to change her stance and express her loyalty towards TMC.
"You cannot ask someone to express her loyalty towards Mamata Banerjee by threatening her. Rather than resorting to such gimmicks, the man from Kanchrapara (Mukul Roy) should focus on building organisation of his party," TMC secretary general Partha Chatterjee.
The BJP central leadership had announced Basu's name as the party's candidate for the byelection yesterday evening. Hours later, Basu told reporters that she is still with the TMC.
The two-time TMC MLA from Noapara assembly seat, however, chose to speak little on the matter and said it was her personal decision to decline the BJP's offer.
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"You can have offers from various political parties. But whether you will accept it or not is a personal decision."
Basu, known to be a close associate of Mukul Roy during his stint with the TMC, was seen holding regular talks with the BJP in the past few days after being denied a ticket from the seat by the Mamata Banerjee-led party.
"She was willing to contest on BJP ticket. But TMC threatened her to change her stance. This instance proves that there is place for democracy in Bengal," said Roy.
The TMC has announced the name of Sunil Singh as its candidate from Noapara.
The Noapara assembly seat fell vacant following the death of Congress MLA Madhusudan Ghose a few months ago.
The bypoll has been scheduled for January 29 and counting of votes will take place on February 1.