The men, whose names were not given, were both arrested last week and are suspected by Belgrade of committing war crimes as members of the Kosovo Liberation Army (KLA) during the 1998–99 war, the ATS news agency reported, citing information from the justice ministry.
The first man, who was arrested in Zurich last Tuesday after Serbian authorities requested his extradition, is reportedly suspected of participating in armed attacks in 1998 against two villages situated in what today is Kosovo.
Serbia accuses him of a range of crimes, including murder, rape and conducting illegal arrests, ATS reported.
The second man was arrested during a routine check in Geneva last Thursday, according to the justice ministry.
Serbia reportedly wants him handed over on suspicion he killed a civilian in 1999.
Both men have refused their extraditions, in a move that will draw out the process and could see the issue go to court.
Complicating matters further, Kosovo insists that it, not Serbia, should handle cases of suspected war crimes committed by Kosovan citizens.
On Friday, Kosovo Justice Minister Hajredin Kuci sent a letter to his Swiss counterpart Simonetta Sommaruga to object to any plans to extradite the men to Serbia, the Sonntagszeitung weekly reported Sunday.
The Swiss justice ministry confirmed to news agency AFP that Sommaruga had received a letter from Kuci, and had responded, addressing his concerns.
In 2012, Switzerland was faced with a similar case.
That time, Bern decided to extradite an ethnic Albanian war crimes suspect to Serbia, since Serbian judicial authorities maintained he was a Serbian citizen.
The suspect, who insisted he was Kosovan, was in the end reportedly released due to lack of evidence.