Nursultan Nazarbayev, Kazakhstan's president, ordered police to investigate his eldest daughter's husband after allegations he was involved in the kidnapping of two former officials of Nurbank, a Kazakh bank in which Aliyev is a shareholder.
On Monday, an international arrest warrant was issued and Aliyev lost his diplomatic immunity a day later after being sacked from his position as ambassador.
Aliyev, a powerful businessman who owns a Kazakh news agency, says the arrest warrant is politically motivated and charges were brought against him after he told his father-in-law that he was considering running for president.
A spokesman for the prosecutor's office in Vienna said a decision would be made within the next 48 hours on whether Aliyev would remain in detention pending the ruling on his extradition.
"Austria has no bilateral agreements with Kazakhstan," Wolfgang Swoboda, prosecutor's office spokesman, said.
"That doesn't mean an extradition is impossible, but it is not quite the same as dealing with another European country, for example."
The Kazakh interior ministry declined to comment but said there would be a news briefing on Saturday.