It is not clear when the judge will issue his ruling although two judicial sources said it should happen within the next few days, Reuters reports.
Falciani, a French citizen and former HSBC computer analyst, in 2008 leaked details of thousands of clients, many of whom he suspected were using their accounts to evade tax.
This information sparked investigations in several countries.
In April this year a Spanish judge freed Falciani after he had been detained in Madrid the day before following a request from Switzerland.
Falciani’s passport was seized and he has to report to the court each week while his extradition request was considered.
In 2008, the French-Italian national passed the stolen HSBC filed to French authorities.
The documents indicated that HSBC helped more than 120,000 clients hide €180.6bn (£161.3bn, $199.8bn) between November 2006 and March 2007.
Falciani moved to Spain in 2012, with a local court rejecting a 2013 extradition request from Switzerland on the grounds that the crime of which he was accused – namely breaking banking secrecy laws – was not subject to prosecution in Spain.
In late 2015, he was sentenced in absentia to five years in prison by a Swiss court for industrial espionage, data theft and violating commercial and banking secrecy.