Inaki Urdangarin, husband of Princess Cristina, King Felipe VI's older sister, was in February sentenced to six years and three months, having been found guilty of syphoning off millions of euros from a foundation.
However, authorities on appeal want to raise the 49-year-old's jail time to 14-and-a-half years, the source said.
Urdangarin is also appealing the sentence, as are five other parties in the so-called Noos case, to the country's Supreme Court. It can confirm, overturn, cut or increase the term and its decision is final.
A court in the Balearic Islands found Urdangarin -- who remains free during the appeal -- guilty of taking millions of euros between 2004 and 2006 from a foundation he headed in the island of Majorca. He was also fined 512,000 euros ($585,000).
Cristina was tried on charges that she helped her husband evade taxes, but the 52-year-old princess was acquitted.
Prosecutors sought a jail term of 19 years and six months for Urdangarin, a former Olympic handball player, during trial.
They want the Supreme Court to add a new five year sentence for embezzlement of public funds, and wants higher jail terms for his corruption, fraud and embezzlement convictions, the source said.
The corruption scandal involving Urdangarin, which broke out in 2010, sparked outrage when Spain was going through a devastating financial crisis, becoming a symbol of an elite out of touch.
It soured the end of the reign of king Juan Carlos, who gave up the throne in June 2014 hoping his son Felipe VI could freshen up the monarchy's image.
Urdangarin and Cristina have been excluded from all of the family's official public appearances since the scandal erupted. They now live in Switzerland.
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