But police spokesman David Furtner told AFP the case was being treated as a “double murder” and not a jihadist killing.
“We currently don't believe that it was an IS-motivated murder or terror attack,” Furtner said.
“It seems the man radicalised himself but there is no third party who ordered him to carry out the killings and IS has not claimed responsibility.”
The suspect attacked the couple in the northern city of Linz on June 30, slitting the 85-year-old woman's throat before stabbing and beating her 87-year-old husband to death.
The brutal nature of the killings shocked many in the country.
Police said the man knew the victims, having regularly delivered their groceries from a shop run by his wife, and believed the elderly couple had links to the far right.
The latest investigations show that he became increasingly radicalised last year and recently swore allegiance on his Facebook page to IS leader Abu Bakr al-Baghdadi.
The suspect, who moved to Austria about 30 years ago, harboured resentment against society as well as Austria's far-right Freedom Party (FPOe), according to police.
“He felt he was always badly treated here because he is a Muslim and blames the FPOe for whipping up negative feelings toward foreigners”, Furtner said.
While Austria has been spared the major attacks that have hit other European countries including France, Britain and Germany, a relatively high number of Austrians have left to wage jihad abroad.
The interior ministry estimates that 300 have left or tried to leave to fight in Syria or Iraq — a figure that is proportionately high in a population of 8.7 million.
Most of those accused of jihadist links in Austria have been of Chechen or Bosnian origin.
There is no indication that the man suspected of murdering the couple had travelled abroad to fight alongside extremist groups.
Austrian authorities have bolstered anti-terror operations since 2014, with 14 people arrested on suspicions of IS links in January raids in Vienna and Graz, the country's second-largest city.
Austria is gearing up for legislative elections in October, which are being closely fought between the social democrats, conservatives and the far right.