The Kronen-Zeitung daily said that the five men knocked at the door in central Vienna of Musar Umarov, former Chechen interior minister under President Ramzan Kadyrov, who however refused to open.
The newspaper gave no other details about the incident but said the men tried to kidnap the former minister.
Umarov, who was also the restive republic's representative in the Russian parliament in Moscow, and his apartment are now being guarded by armed police, the newspaper said.
A Vienna police spokesman told AFP only that an "incident" took place last Thursday and that a case of alleged "dangerous harassment" was being investigated.
In January 2009 Chechen dissident Umar Israilov, who had sought asylum in Austria, was gunned down in broad daylight on a Vienna street.
Israilov had been due to testify in a key European torture case against Kadyrov when he was killed. He was a former member of Kadyrov's security forces.
A 2010 Austrian police report concluded that Kadyrov had ordered the man kidnapped, with prosecutors saying the Chechen leader had given explicit instructions that he be killed if he resisted.
In 2011 three ethnic Chechen men were convicted in Vienna for the murder. Via his lawyer, Kadyrov denied any involvement.