Fr Tom Uzhannalil was kidnapped by gunmen in the Yemeni city of Aden earlier this month, after they stormed a care home run by nuns and murdered 16 of them.
It was subsequently reported by a group of Catholic sisters in South Africa that Islamic State had captured Fr Tom, and that they were planning to crucify him on Easter Day.
Austrian media have now reported that the Archbishop of Vienna, Cardinal Christoph Schonborn, confirmed the priest's death in a sermon during evening Mass last night on Easter Sunday.
Premier has been unable to contact the Archdiocese of Vienna to confirm exactly what Christoph Schonborn said regarding his current condition, but the archdiocese has posted a press release on its website regarding Fr Tom in German.
Most Revd Dr Bernard Moras, the Archbishop of Bangalore where Fr Tom is from, told Premier on the telephone that they have received no word of his death "as of now".
The Archbishop also said reports that Fr Tom has been crucified are currently "rumours", and that "people are making news without confirmation".
He also said the archdiocese was trying to get information on Fr Tom's condition, however efforts so far have proved futile and they "cannot get it confirmed".