Kovind is expected to win the presidential race given that the BJP and its allies have a majority in electoral college comprising Members of Parliament and members of legislative assemblies and councils of all states.
A formal announcement of the winner is expected by 5 pm. The voting took place on Monday.
Counting began at 11 am with the ballot box of Parliament House being opened first, followed by ballot boxes received from states in alphabetical order.
An Election Commission official, who has witnessed previous two presidential polls, said usually results are declared around 5 PM.
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Close to 99 per cent voting was recorded for electing India's next president.
Thirty two polling stations, including the one in Parliament House, were set up in various states.
A total of 4,896 voters -- 4,120 MLAs and 776 elected MPs -- were eligible to cast their ballot. MLCs of states with legislative council are not part of the electoral college.
While the value of an MLA's vote depends on the population of his or her state, the value of an MP's vote remains the same at 708.