Mr Drnovsek is head of the Liberal Democrats and he is being backed by Mr Kucan.
Even though his victory in the run-off round is widely predicted, the growing popularity of Ms Brezigar could make her a tougher challenger than expected.
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None of the other seven candidates won more than 10% of the vote, French news agency AFP reported.
Transition
The election marks the end of an era for Slovenia, with the retirement of the man who led the country to independence from Yugoslavia.
Mr Kucan, the country's president since 1990 and referred to by many Slovenes as "the father of the nation", is standing down after more than a decade in office.
Mr Drnovsek was always the clear favourite; prime minister since 1992, he is credited with steering the country through its transition to a market economy.
If elected for the largely ceremonial post of president, his main task will be to take Slovenia into the European Union and Nato - negotiations are due to be completed in the next few months.
Slovenia escaped almost unscathed from the disintegration of the old Yugoslavia - its self-proclaimed war of independence in 1991 lasted 10 days and claimed a handful of lives.
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