Talking to reporters in Bangalore, he said he had received a letter from Governor T N Chaturvedi asking him to take a decision on the issue on or before January 27.
Kumaraswamy, son of JD (S) supremo H D Deve Gowda, had submitted a letter to the Speaker stating that he had been elected the new Janata Dal Legislative Party leader.
Krishna declined to comment when asked whether he would follow the precedent set by him during the election of M P Prakash as the JDLP leader after the ouster of Mr Siddaramaiah from the post.
Asked about his visit to Gowda's residence, he described it as a courtesy call. "I don't talk politics with Mr Gowda after I have become the Speaker."