Pro-union leaders say Mr Puigdemont, who is in self-imposed exile, cannot lead the region "via WhatsApp or as a hologram".
Mr Puigdemont fled to Brussels in self-imposed exile after he was sacked by the Spanish government in October for his role in staging an illegal referendum and unilaterally declaring independence.
A deal for Mr Puigdemont’s party, Junts per Catalunya (Together for Catalonia), and Esquerra Republicana de Catalunya (Republican Left of Catalonia) to support the former president was reached in Brussels on Tuesday evening.
Spanish Prime Minister Mariano Rajoy called a regional election on 21 December to resolve the region's political crisis, but results proved inconclusive after the pro-independence parties failed to get over 50% of the vote, despite claiming a narrow majority of parliamentary seats.
Junts per Catalunya representative Jordi Xucla told Spanish national radio: "The December 21 result gave us the mandate to reflect the majority. The presidential candidate will evidently be Puigdemont."
An Esquerra Republicana de Catalunya spokesman said Mr Puigdemont will propose to speak via video conference or get a fellow party member to read the speech required by regional leadership candidates.
Dismissing the suggestion, the leader of the anti-independence Ciutadans (Citizens) party said "a person who is fleeing justice can't be the president".
Ines Arrimadas added: "It's evident that for governing Catalonia you have to be in Catalonia - you can't do that via WhatsApp or as a hologram."
The new Catalan parliament will hold its first session on 17 January, the first step in reinstating local government.
Once the parliament is formed, potential leaders of the regional government will put themselves forward for a vote of confidence, although it could take months for a new government to emerge.
The other main potential candidate to represent the pro-independence parties would be ERC leader Oriol Junqueras, who is serving a custodial sentence in a Madrid jail.