Marian Lesko, a columnist for the daily Sme newspaper, said he expected the results of Saturday's election to mirror those of the first round.
"Despite the first round results, I don't expect a change, and the second round will be in favour of Gasparovic as well." he said.
About 6,000 polling stations opened at 7am local time (05:00 GMT) and more than four million eligible voters have until 10pm (20:00 GMT) to cast their ballots with results expected during the night.
The election is seen by some analysts as a test of support for Robert Fico, the country's prime minister, who has endorsed Gasparovic.
The role of the president is mostly ceremonial in Slovakia, where a parliamentary democracy was established in 1993, following the break up of Czechoslovakia.