He said Krishna would be inducted into the party in the presence of BJP National President Amit Shah and other central leaders.
Krishna, on the other hand, has neither commented nor denied reports of Yeddyurappa claiming that he would be joining the saffron party.
The 84-year-old Krishna had announced his resignation from the Congress on January 29, saying the party was in a "state of confusion" on whether it needs mass leaders or not.
Krishna, who was Karnataka chief minister from 1999 to 2004, had returned to state politics after stepping down as the minister for external affairs in 2012. He had also served as Governor of Maharashtra.
The bypolls are scheduled to be be held on April 9. The Nanjangud seat fell vacant after the resignation of veteran Congress leader V Srinivas Prasad in December 2016 as he was disgruntled with the Congress after he was dropped from Siddaramaiah's cabinet. Prasad later joined the BJP.
The Gundlupet seat fell vacant after the death of MLA H C Mahadeva Prasad on January 3, who was Cooperation and Sugar Minister.
Yeddyurappa said he would be in New Delhi on Tuesday to attend an internal party meeting.