The 54-year-old is serving a suspended jail sentence for electoral fraud, which in theory under Romanian law bars him from office
"I've listed the (prime ministerial) criteria before the election campaign began so there wouldn't be any discussions afterwards, and they remain the same," Klaus Iohannis said at a press conference in the capital Bucharest.
Dragnea's corruption-tainted Social Democrats (PSD) staged a thumping comeback on Sunday by sweeping 45.3 percent of the vote, a year after anger over a deadly nightclub fire drove them from office.
Their centre-right rivals National Liberal Party and the Save Romania Union, newly created by a mathematician-turned-activist, trailed on a combined 29.5 percent.
As chief of the biggest party, Dragnea would be the logical choice for prime minister.
However the 54-year-old is serving a suspended jail sentence for electoral fraud, which in theory under Romanian law bars him from office.
He nonetheless suggested Sunday that he wanted the top job.
"I do not intend to gift my votes to someone else, whether it be a person or an institution. I ran the campaign, the party, it was an enormous responsibility," he said.
Analysts said the PSD may seek a way around the issue by trying to amend the law.
But the president warned he would stick to his guns even if legislation was changed.
He added that he would hold talks with all elected parties on Wednesday.
The new government will be sworn in at the earliest on December 19.
Mass protests in the EU's second-poorest country after the disco blaze on October 30, 2015 that claimed 64 lives drove premier Victor Ponta and his Social Democrats to resign.