Labor-Party candidate Peter Obi is also expected to do well, AFP reported.
In Africa's most densely populated country with a total of 220 million people, 87 million are eligible to vote.
The elections are taking place under tight security measures. Armed militias are active in some parts of the country, including Boko Haram terrorists.
Nigeria's borders will be closed on election day and, with a few exceptions, cars will not be allowed to drive either.