Puigdemont's visit to Denmark could help him avoid problems in Belgium, where European citizens can live without a residency permit for three months, after which they theoretically have to leave.
At the time, the Supreme Court had issued an global arrest warrant against him, but withdrew it in December to avoid Belgium granting him asylum.
After taking the decision, the Spanish court also noted that the withdrawal of the arrest warrant also prevented more than one European jurisdiction overseeing the case.
Spanish authorities are still investigating Catalan officials for possible rebellion and sedition charges.
Mr Puigdemont is on a trip to Denmark from Belgium, where he fled in October.
"President Puigdemont never dismissed the possibility of presenting and submitting his candidacy in person", the lawyer told Catalonian public television, adding that his client was "aware of the risks he faces".
Foreign Minister Alfonso Dastis said yesterday in Brussels that 'proposing a fugitive of justice to head the Catalan government was not the 'best start for the new parliamentary term in Catalonia.
Puigdemont is trying to return to his position as Catalan's president after the region's snap election in December saw secessionist parties retaining their majority in parliament and hopes to read his speech in the regional parliament debates with the help of one of his MPs. The Faeroes are holding a referendum on a new constitution on April 25. Prime Minister Mariano Rajoy reiterated on Saturday it would be considered "illegal".
Roger Torrent, the speaker of the newly elected parliament, said on Monday that Puigdemont has been nominated as a candidate to govern the region again.
A Faeroese lawmaker invited Puigdemont to the Danish Parliament on Tuesday.
The Spanish government has threatened to arrest him the moment he sets foot back in Spain.