Puigdemont fled to Brussels shortly after Catalonia declared independence in October.
Catalonia's parliament is set to vote on the Spanish region's new president on Tuesday, according to the president of the legislature.
"Puigdemont's status does not allow him to attend a [parliamentary] session [to discuss potential candidates for Catalan president] as he is wanted".
The central government in Madrid has said it will seek to block any such move in the courts.
The Catalan parliament is expected to hold a vote to approve the region's new leader on January 31.
The 55-year old former journalist potentially faces decades of jail in Spain if he is convicted of the charges levelled against him, including rebellion and sedition, for organising the referendum and declaring Catalonia's independence.
Extra police are stationed at airports, ports and the border with France in case Mr Puigdemont tries to stage a dramatic return...
Catalonia's newly elected parliamentary speaker nominated Puigdemont on Monday as the sole candidate for regional president, defying Spanish government warnings.
Rajoy called snap regional elections for Catalonia in December after assuming control of the government.
Several days later, separatist leaders were charged for their attempt to break from Spain via a banned independence referendum, but by then Puigdemont and several of his former ministers were already in Belgium. The State Council referred to lack of grounds to contest the candidacy preventively and added that if the pro-independence leader would appear before the chamber was still unknown.
The government's decision to appeal directly to the constitutional court comes after the Council of State - the supreme consultative council of the Spanish government which advises on serious issues - advised against it on Thursday.
"We will use this prerogative (the constitutional court) to stop Puigdemont's candidacy progressing and producing irreparable damage", Sainz de Santamaria was quoted as saying.