Will he come back and risk jail for his role in Catalonia's independence drive as former regional president, or will the pro-independence camp pick someone else?
The dilemma comes after three pro-independence groupings won an absolute majority in parliament in elections last month called by Madrid to try and end months of turmoil as Catalan leaders attempted to break away from Spain.
Puigdemont's "Together for Catalonia" list got the most seats out of the three parties, which are expected to join forces again, making him the natural candidate for the presidency.
Exile and jail
But they face a significant challenge as Puigdemont and four of his former ministers who were also re-elected are in Belgium.
They went there after being sacked by Madrid over a unilateral independence declaration on October 27th, and are wanted in Spain on charges of rebellion, sedition and misuse of public funds.
Three others, including former vice president Oriol Junqueras, are in jail pending a probe into the same charges.
Puigdemont's list won 34 seats in the 135-seat regional parliament.
Junqueras's ERC party got 32, and the small far-left CUP party won four, giving these pro-independence groupings an absolute majority of 70 seats.
But if those in Belgium or prison can't officially take their posts, the separatist camp will lose its majority.
On Friday, the Supreme Court rejected a demand by Junqueras to be released.
The court is unlikely to be lenient towards the other separatists in jail, having argued for Junqueras that there is a risk he would "re-offend as there is no sign that the defendant has any intention of abandoning the route he has followed until now."
Those in Belgium are unlikely to come back as they face arrest.
A lack of majority will be a major problem for Puigdemont, not least because he first needs to ensure he has allies in the strategic "presidents bureau" of the Catalan parliament, which makes sure assembly rules are respected.
This bureau -- the members of which are voted by parliament -- would have to allow him to present his programme to parliament via videolink from Belgium and be elected without being present.
So in order for separatists to keep their majority, at least six out of the eight in Belgium or prison will likely have to renounce their seat and be replaced by others on their list.
The other option would be to get the support of far-left grouping Catalunya en Comu, which won eight seats and opposes Madrid's policies even if it is against independence.
Any decision will have to be taken before January 17th, when the first session of the new Catalan parliament takes place.
Leaving these challenges aside, Puigdemont also need to address niggling doubts within his own separatist camp, and particularly among those in Junqueras's ERC party.
"We don't know how they (Puigdemont and the elected officials in Belgium) plan to do it, if they will come or not," an ERC source who refused to be named told AFP, adding the videolink option was "strange."
And ERC is already thought to be considering a "plan B."
"The competition between both pro-independence groupings is bigger and bigger," wrote Enric Juliana, an influential Catalan journalist, in the La Vanguardia daily on Friday.
Finally, if Puigdemont managed to overcome the divisions and procedural rules to be re-elected president of Catalonia, how will he govern the region?
"Carles Puigdemont has said that if he is officially nominated, he will come back," said a source from his party, who refused to be named.
But won't he immediately be arrested?
"If he comes to the door of the Catalan presidency surrounded by 500 mayors who support him, will the Spanish government really arrest him?," the source asked.
"In any case, if he comes and he is arrested, his term in office ends and there will be new elections in three months."