Mr Puigdemont fled to Brussels after Spanish authorities levelled charges of sedition, rebellion and misuse of public funds against him for his role in the region's disputed independence referendum.
Pro-independence parties including Mas' PdeCat won the most seats 70 out of 135 in the Catalan parliamentary election in December.
The two separatist parties hold the majority in the new regional parliament.
Mariano Rajoy, Spain's prime minister, called the election hoping that voters in the prosperous region would halt the drive for independence.
Mr Puigdemont, who is in self-imposed exile in Belgium, may either return and risk arrest or be sworn in from overseas.
Pro independence parties Junts per Catalunya (Together for Catalonia) and Esquerra Republicana de Catalunya (ERC) (Republican Left of Catalonia) said on Wednesday (10 January) they would support Puigdemont's return to the top job. Those leaders remain out of the country, and Puigdemont has said if he's re-elected, he would discharge his duties remotely, via a video linkup such as Skype.
Pro-independence parties secured a slim majority of seats but failed to win more than 50 percent of the popular vote, meaning there is still no end in sight to the months-long, and increasingly bitter, impasse.
Ines Arrimadas, the leader of Ciudadanos (Citizens), which favours unity with Spain, said a fugitive from justice could not be a leader in Catalonia. Insisting that such methods would be illegal, Mr Maillo said anything other than a traditional investiture - in which a president presented himself and his programme to parliament for a vote - would be "a real mockery, first of the Catalans, and then of the rest of the parliamentary groups".
The parties' announcement Wednesday raises the specter of a renewed push for independence - and also raises hard questions about how, exactly, Puigdemont might go about governing.
The deal - reached over dinner in Brussels on Tuesday - would allow Puigdemont to deliver his acceptance speech this month either by videoconference from Belgium or by having another lawmaker read it in the Catalan Parliament on his behalf, according to the Catalan radio station Rac1 and other outlets.
But Puigdemont remains in self-imposed exile in Brussels after he fled to Belgium with four of his cabinet members when Madrid imposed direct rule on Catalonia and sacked his government following an October 27 declaration of independence.