Separatist allies announced on Saturday they would try to have Puigdemont, now in Germany after being detained there in March on a European arrest warrant, re-appointed as president by next week after the regional parliament voted through reforms allowing him to take the role without being present.
If Mr Torra fails to win an absolute majority in the first-round vote in the parliament, he will face a second-round ballot on Monday, needing only a simple majority.
On Friday, the exiled former Catalan president, Carles Puigdemont, announced from Berlin his decision to name Mr Torra as his successor.
Quim Torra, the man chosen by ousted Catalan president Carles Puigdemont to be his successor, may be a newcomer to politics but he has always been a staunch separatist.
Backing unilateral independence over the negotiated exit favoured by larger separatist parties, the CUP has previously broken ranks with the pro-independence block.
Separatist events maintained a slim majority in regional elections in December, however Spanish courts have blocked efforts to elect two separatists in jail awaiting trial and fugitive ex-chief Carles Puigdemont.
The Spanish legal system has charged Puigdemont and other separatist leaders with a range of offenses over their roles in the independence push.
Torra is a newcomer to politics. "Our group proposes member of parliament Quim Torra to be president of the Catalan government so he can take on this responsibility in the next few days and so that a government can be formed immediately", Puigdemont said.
"He is the most radical that Puigdemont could find and the only one who voluntarily accepted to be the puppet of Mr. Puigdemont", she told reporters.
A German court last month dismissed the extradition request for Puigdemont on the rebellion allegations and released him on bail.