The goal of the testing scheme is to allow the country to emerge from lockdown before Christmas.
In a study, 28 percent of those surveyed said they wanted the scheme to be mandatory.
A further 69 percent said they wanted the scheme to be voluntary, while four percent said they did not know.
The results come from a survey carried out by television network ATV.
Despite the effectiveness of a nationwide mandatory testing program, Austrian Health Minister Rudolf Anschober has previously said any mass testing regime would be voluntary, reported Kronen Zeitung.
Anschober did however leave the door open to the possibility of requiring people in specific professions to be tested, i.e. medical staff or support staff in nursing homes.
Austrian media reports that medical workers would also be one of the targeted groups for testing.
In Slovakia, anyone who refused to be tested were subject to a strict curfew and were not allowed to work.
Mass testing to 'save Christmas'
“We know it's something close to many people's hearts to be able to celebrate in a half decent way with at least a small number of their loved ones,” Chancellor Sebastian Kurz said.
Kurz told public broadcaster ORF that “we have decided here in Austria… to take a similar step”.
“We want to deploy mass tests at the end of the lockdown in order to enable a safe re-opening in schools and other areas,” Kurz said, adding that in the first instance testing would be focused on groups such as teachers.