Radev is followed by Atanas Gerdzhikov, representing the center-right party GERB, who has 24 percent.
Earlier, an exit poll conducted by the Market Links polling agency showed that Radev has 49.5 percent, while Gerdzhikov has 26.5 percent.
If Radev fails to win over 50 percent of the votes, a runoff election will take place on November 21.
Meanwhile, the right-wing GERB-SDS coalition is in the lead in the parliamentary election with 24.8 percent, followed by the We Continue the Change party with 24.1 percent, according to an Alpha Research exit poll.
In contrast, the Gallup International Balkans poll showed that We Continue the Change has 26.3 percent, while GERB-SDSis second with 23.1 percent.
Bulgarians went to the polls on Sunday to elect a new parliament and a new president. The turnout was estimated at below 40 percent.