The source said judges at the court voted to uphold an appeal by Juan Carlos against the suit brought by Ingrid Sartiau, a housewife who claims he fathered her in the mid-1960s before he became king.
In January the court said it would take on the suit lodged by Sartiau after examining documents offered as proof of a relationship between her mother and Juan Carlos.
But the former King apealed against the decision for it to be heard.
A second suit lodged by Catalan waiter Alberto Solá Jiménez, 58, will not be heard with the civil section of the powerful court citing a lack evidence.
Mr Sola and Mrs Sartiau teamed up in 2012 when they underwent DNA tests that showed there was a 91 per cent chance that they had one parent in common
The cases took so long to be lodge because while he was monarch, Juan Carlos, 77, enjoyed constitutional immunity until he abdicated in June last year when he lost that special legal status.
However, he continues to enjoy a special form of legal protection known as 'aforamiento' which means cases against him can only be heard in the country's top courts.
Juan Carlos I abdicated after a series of health problems and various scandals within Spain's Royal Family, notably the criminal case against his youngest daughter, Princess Cristina, and her husband Iñaki Urdangarin.
In a first for the royal family, Cristina is set to appear in court on two counts of tax fraud, each carrying a sentence of four years.