Some of the non-attendees have stated that Danish politicians should not interfere with Spain's domestic politics, while others have cited prior commitments.
But Holger K. Nielsen, former Foreign Minister and current foreign policy spokesperson with the left-wing Socialist People's Party, said ahead of the meeting that politicians have an obligation to take a stance on international issues.
"It is important to have a discussion with those you do not agree with. I am not particularly in agreement with Puigdemont and the demand for separation from Spain. But democracy is also about speaking to people whose views you do not share," Nielsen said.
Puigdemont was sacked by Madrid after the Catalan parliament declared independence on October 27th, following an October 1st referendum that was not recognised by Spain's central government.
Currently based in Brussels, the former regional leader has been in the Danish capital since Monday, when he took part in a debate on Catalonia at the University of Copenhagen.
On Sunday, Spain's prosecution service said it would "immediately" have a supreme court judge issue a warrant for Puigdemont's arrest if he travelled to Denmark, and urged Copenhagen to hand him over.
MP Magni Arge of the Faroe Islands Tjóðveld (Republican) party invited Puigdemont to meet with lawmakers from various parliamentary committees at Denmark's Christiansborg parliament.
The Faroe Islands are an autonomous territory within Denmark.
But no representatives from any of the three government parties - the Liberals, Conservatives and Liberal Alliance - will be in attendance.
Neither will the largest opposition party, the Social Democrats, who noted that the Spanish government would also not be represented.
Nielsen said that the meeting did not constitute an endorsement for Puigdemont's stated aim of Catalan independence.
"I regularly meet the Israeli ambassador. That does not mean I support Israeli settlement policies," he said.
"You have to meet people you do not agree with," he added.
Catalonia's parliament on Monday proposed Puigdemont as president of the region following a snap election in December in which separatist parties again won an absolute majority.
During his first foreign visit since leaving Spain to live in voluntary exile in Brussels on October 30th, Puigdemont on Monday told students at the University of Copenhagen the EU showed "failures" in the face of crises both inside and outside its borders.
"The EU has been a success in promoting freedom, democracy, prosperity and welfare on our continent," he said. "However, we're all aware of each failure every time there is a crisis.
"We saw it in Greece, we saw it in Ukraine, we saw it with the refugees and now we see it with the failure to defend the fundamental rights in Catalonia," he added.
He also said that he would "soon" form a new Catalan regional government, despite opposition from Madrid. He gave no further detail regarding when that would happen, but said he would say more on the issue during his visit to the Danish parliament.