The final Cabinet approval, if it comes, would happen after the country's general election on Sunday, people familiar with the matter told AP.
Anti-drug prosecutors had appealed a mid-September decision by the Spanish National Court rejecting the extradition to the United States, where he is wanted on drug smuggling and other charges.
The extradition needs to be cleared next by the Spanish Cabinet, which typically holds weekly meetings every Friday.
Appeals can be filed before the country's Constitutional Court and the European Court of Human Rights, but that wouldn't necessarily stop the extradition.
The DEA referred questions to the U.S. Southern District Court in New York, which had no comment on the matter.