Catalonia, worth a fifth of Spain's economic output, has been unable to form a government since a regional election in September due to disagreements between the winning, pro-independence coalition parties.
If a new candidate is not chosen before Jan. 9, new regional elections will be called automatically.
The failure to form a Catalan government echoes a political stalemate gripping Spain at a national level following an inconclusive national election on Dec. 20 and increases the likelihood all Spaniards will return to the ballot box this year.
"I sincerely don't know what could possibly happen in the next five days, but I believe that the best that could happen is that (acting regional head Artur) Mas drops his independence drive and, as that doesn't seem possible, there's no alternative to elections," Rajoy said in a radio interview, Reuters reported.
On Sunday, a minority party in the regional coalition, CUP, said it would not support the business-friendly Mas in his bid for another term, a red line for partners Junts pel Si which suggested on Monday it would stand by its candidate.
The protracted efforts to choose a Catalan leader has dampened a separatist movement that at its peak drew one million people onto the streets of Barcelona, and has highlighted divisions between supporters.
Rajoy also said he had no plans to stand down as a candidate as prime minister and reiterated that there was a possibility of a pact with traditional political rivals in order to form a government.
He said there were more policy similarities between his conservative People's Party (PP) and the Socialists (PSOE) than there were differences, adding that there were no red lines over pacts with them or the liberal Ciudadanos.