Kovind, 71, who was announced as the presidential nominee by the Bharatiya Janata Party (BJP) chief Amit Shah on June 19, called on Vajpayee at his Krishna Menon Marg residence. Kovind was accompanied by his wife.
Following his nomination, Kovind has been meeting several senior BJP leaders. He was once a general secretary of the party. On Wednesday he met BJP veteran L K Advani and Murali Manohar Joshi in New Delhi.
Kovind will file his nomination papers on Friday, following which he was expected to reach out to the opposition parties for their support.
The Presidential election is scheduled for July 17.