He made the statement in an attempt to unblock a political impasse as the region remains without a fully functioning government.
Puigdemont will propose pro-independence campaigner Jordi Sanchez, now held on remand in Madrid on charges of sedition, as an alternative candidate, the paper said.
Announcing he was provisionally withdrawing his candidacy, he said that decision "is founded in one reason only - under current conditions it's the way to get a new government under way".
'I know that the path we have ahead is long and fraught with difficulties'. Sanchez now resides in a Madrid prison.
Catalonia has been ruled by Madrid since October, when Spanish Prime Minister Mariano Rajoy used constitutional powers to take over, after the region's parliament declared independence in the wake of a referendum.
The Spanish government moved in immediately, stripping Catalonia of its prized autonomy, sacking its regional government, dissolving its parliament and calling snap elections on December 21.
"The honourable President Puigdemont has won enough support at the ballot box to be allowed to be voted in as president", said Quim Torra, a Junts per Catalunya lawmaker.More news: Israel arrests family member of jailed Palestinian teen
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As such, he was the separatists' favoured candidate to lead Catalonia again, arguing he could govern the region remotely.
Separatist parties in the regional parliament insisted earlier on Thursday that Mr Puigdemont is their legitimate leader despite a ruling by Spain's Constitutional Court that he can not take office because he is not in Spain.
At the end of January, the Catalan parliament's speaker - also a separatist - postponed a key vote to reappoint him as president.
Carles Puigdemont has withdrawn himself from consideration as leader of Catalonia.
Madrid called a snap election for December a year ago in hope of having a more moderate Catalan government to deal with, but its plan backfired when the region voted a majority of pro-independence MPs into parliament, maintaining the status quo. However, the motion stops short of validating a failed declaration of independence on October 27.
"That is insane. What is necessary to do is to elect a person, who is in Spain, who is not in prison, who has no problems with justice and respects the law", Spanish Prime Minister Mariano Rajoy told the Telecinco broadcaster.