The newspaper cited sources close to the Catalan agriculture ministry.
Two cases have been confirmed and 12 others have shown signs they may also have the disease but are undergoing tests to confirm this.
If confirmed, it would bring the number of infected animals to 14.
The Catalan government, which declined to confirm the number of cases, on Sunday, December 14, requested the help of specialists from the army to contain the outbreak.
About a third of Spanish pork export certificates have been blocked after the first outbreak of swine fever in Spain — the European Union's top pork producer — since 1994, Spain's agriculture minister said on Saturday.
“Of the 400 export certificates to 104 countries, a third are blocked. We are working to open them as quickly as possible,” Agriculture Minister Luis Planas told a press conference.
Mr Planas said the value of the country's pork exports was 8.8 billion euros ($A15.7 billion) a year.
“Our task is to keep international markets open,” he said.
African swine fever is not harmful to humans but spreads rapidly among pigs and wild boar.
A number of countries have already reacted to its spread in Spain.
Taiwan's agriculture ministry said on Saturday, December 13, it had banned all pork products and live pig imports while China has banned pork imports from Barcelona province, a Chinese Customs document seen by Reuters showed.
The United Kingdom on Friday, December 12, said it would temporarily stop imports of pork meat from Catalonia, and Mexico has suspended imports of pork products from Spain.
