Puigdemont, living in self exile in Belgium and wanted in Spain, announced last week that he was abandoning his bid to return as regional president in an attempt to unblock Catalonia's political crisis.
The move could pave the way for the Spanish region to get a fully functioning government and regain its autonomy after Madrid took full control of Catalonia following a banned independence referendum in October.
The regional assembly's head, Roger Torrent, was scheduled to meet with representatives of the seven parliamentary groups on Monday to pick a new candidate to replace Puigdemont.
The only name put forward so far by Puigdemont himself is Jordi Sanchez, head of the hugely influential pro independence ANC citizens' group.
Catalan parliament to meet, but without sacked leader
But this is likely to be difficult as Sanchez has been in prison for more than four months as he is investigated for sedition, one of four separatists jailed over their role in the independence drive.
Sanchez isn't a favourite among some of Puigdemont's separatist allies either, with the smallest of the three pro independence parties, the Popular Unity Candidacy (CUP) threatening to block his nomination.
With both Puigdemont and another Catalan deputy, Toni Comin, in Belgium and unable to participate in the vote, Sanchez would not have the necessary support.
For the time being, Catalonia, which has a population of 7.5 million, remains without an effective government and under direct control from Madrid, which means it cannot manage its own healthcare or education as it did previously as a semi autonomous region.
Once a new government is installed, however, Catalonia will recover its autonomy.
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