Bakhtiar Ali, one of the sixth-generation descendants of Prince Mooniruddin, who was one of Tipu's sons, told PTI that the minister's comments were "baseless and shameful".
"Such derogatory remarks are unacceptable. He is making such cheap comments for his own political gains. We are consulting lawyers and will seek legal action against him. We might file defamation suit against him," Mr Ali said.
The BJP minister, in a tweet on October 21, had conveyed to the Karnataka government not to invite him to the "shameful" event of Tipu Sultan Jayanti on November 10.
In 2016, Mr Hegde had flayed the state government for celebrating Tipu Jayanti despite opposition from some sections of the society living in coastal belts of Karnataka and Kodagu areas, claiming that the ruler was "against Kannada language and anti-Hindu".
Subsequently, Mr Hegde was arrested for threatening to disrupt celebrations in Uttara Kannada district.