During his travel from Belgium to Denmark, the Madrid prosecutor's office requested that he be arrested but the preliminary investigative judge of the Madrid Supreme Court, Pablo Llarena, rejected the request for another European arrest warrant.
The Catlonia leader and five of his ex-ministers all traveled to Belgium following a unilateral declaration of independence in the Catalan parliament on October 27, considered illegal by Spanish courts.
The Spanish prosecution asked the Court to reinstate the European Union arrest warrant, as Puigdemont had arrived in Denmark to deliver a speech at the University of Copenhagen, the El Pais newspaper said.
At home, however, he risks arrest on charges of rebellion, sedition and misuse of public funds.
His proposed appearance at the debate in the Danish capital comes while Puigdemont is trying to be reinstated as the regional president of Catalonia. Madrid made the request following Puigdemont's first trip outside of Belgium.
Copenhagen police spokesman Riad Tolba told The Associated Press that no arrest warrant has arrived yet, so Mr Puigdemont has not been arrested.
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Mr Torrent said he was "conscious of the warnings that weigh upon him, but I am also conscious of his absolute legitimacy to be candidate".
In the report accompanying his decision not to issue the arrest warrant, Mr Llarena suggested that Mr Puigdemont had travelled to Denmark hoping to be arrested in order to make a political point ahead of what is likely to be a highly charged investiture debate.
Puigdemont flew Monday to Copenhagen from Belgium, where he has been since fleeing a Spanish investigation into the Catalan parliament's secession declaration a year ago.
But Spanish Prime Minister Mariano Rajoy reiterated Saturday that governing Catalonia from overseas would be "illegal".
The controversy came as Mr Puigdemont was nominated by the speaker of the Catalan parliament, Roger Torrent, to head the regional government on Monday.
A Spanish Supreme Court judge withdrew a Europe-wide warrant in December, saying it would complicate the Spanish legal investigation and its removal would allow Spain to gain full control over the case.