Torrent insisted Puigdemont was still the candidate after separatist parties maintained their absolute majority in December regional polls, led by the separatist leader's grouping.
But he faces arrest as soon as he steps back into Spain over his role in the failed independence bid, and Madrid has vowed to block his return.
Meanwhile, the separatist camp is in disarray over Torrent's decision to delay the vote and Puigdemont's resolve appears to be foundering.
So what next?
How long can impasse last?
Under electoral rules, the Catalan parliament had until Wednesday this week to hold its first session at which lawmakers would re-appoint Puigdemont, the only candidate for the presidency.
And if they failed to agree on him or pick a new president in the following two months, new elections would be called.
But that countdown has been put on hold as Torrent waits for the Constitutional Court to decide whether to examine Madrid's request to block Puigdemont from being re-appointed -- a decision due in the coming weeks.
If the court rejects it, the countdown will start over.
If it accepts it, the situation could remain paralysed for months as the court examines the issue in depth and decides whether or not to block his candidacy.
During that time, Catalonia would continue under the control of the central government, which imposed direct rule on the wealthy semi-autonomous region on October 27th after the Catalan parliament declared independence.
A future with Puigdemont?
Catalonia's president from January 2016 to October last year, when he was sacked by Madrid, Puigdemont maintains that he is the only candidate to lead the region again.
Torrent's decision to delay his appointment severely deepened divisions within the separatist camp.
Torrent is a member of the separatist ERC party, an ally of Puigdemont's Together for Catalonia grouping.
Puigdemont and his grouping want to breach Catalan parliamentary rules by having lawmakers re-appoint him even in absentia, a move that Madrid fiercely opposes.
But ERC would rather avoid another frontal clash with Madrid and form an operational regional government that would lead to the lifting of direct rule.
"It was going to generate chaos and wasn't going to go anywhere," an ERC source who requested anonymity told AFP, justifying the delay of Puigdemont's appointment.
"We can't be swept along by those in Belgium, we need to stop and look at how we can have a government for real."
But even if separatist parties end up reaching a deal, that would not be the end of Puigdemont's problems.
If he comes back to Spain, he faces arrest and jail. Any attempt to be re-appointed by video link from Belgium will be contested by Madrid and probably suspended by the courts.
And the clock is also ticking for him.
If the probe into separatist leaders for rebellion and sedition goes to trial, those charged -- including Puigdemont -- could be barred from office as a precautionary measure.
A screenshot of alleged messages between Puigdemont and Comín broadcast by Telecinco on Wednesday.
The central government and anti-independence parties in Catalonia are increasingly calling for an alternative candidate to be considered to lead the region.
"Torrent must open a round of talks (with parties) to save the situation generated by Mr. Puigdemont," Spain's Deputy Prime Minister Soraya Saenz de Santamaria said Wednesday.
Puigdemont himself appeared to be throwing in the towel on Tuesday, according to private mobile phone messages caught on camera by a Spanish television reporter.
In these, he considers that he has reached the end of the road having been "sacrificed" by his peers.
Puigdemont has not denied he sent those messages, but insists he is still the candidate.
No separatist party is publicly proposing to ditch him but many alternative candidates are appearing in the press.
Ultimately, until the Constitutional Court makes its decision as to whether to examine Madrid's request to block Puigdemont, the ball is in Torrent's court.
He could decide to keep him as candidate and hold the parliamentary vote to re-appoint him, or nominate another candidate.