"He gave him the offer. Ganguly neither said yes nor no to the proposal. He said he will think and then decide on whether to fight the elections or not," Sinha, also the party's national executive member, said.
Varun, the national general secretary of BJP, is also the party's observer for West Bengal.
When asked to comment on a newspaper report that BJP's prime ministerial candidate Narendra Modi has promised to make the Bengal sports icon the sports minister in the cabinet if the party comes to power, Sinha denied it.
"All that is false," he said.
In the Trinamool Congress-ruled Bengal with 42 seats, BJP has a solitary presence in Darjeeling.
Ganguly, however, could not be reached for a reaction to the report.