The Vatican, which announced Murad's death last week, has said it has no knowledge of the video, posted Monday by Catholic Online, CNN reported.
The Daily Telegraph of London reported local sources said Murad was shot.
"It is very important the world knows that Christians are being murdered for their faith, and that martyrdom isn't an ancient phenomenon," the website said. "This should make it clear to Christians around the world what jihadists are about. Make no mistake. Catholics and Christians around the globe are under dire threat, particularly from the spread of militant Islam. Until the threat is recognized and taken seriously, martyrdoms like this will continue."
The Telegraph said the video, which shows two men being beheaded as a crowd yells "God is great," is too grainy to identify any of the prisoners depicted. The newspaper said it may be an older video.
The newspaper said its sources said Murad "died when he was shot inside his church." The sources said that occurred June 23 in Ghassaniyeh, a Christian village near the Turkish border.
About three-quarters of Syrians are Sunni Muslims. The family of President Bashar Assad are Alawites, members of a minority Muslim sect, and there are also Shiite communities and Christians.
In its statement last week, the Vatican said Murad died defending his church, CNN reported. The Rev. Pierbattista Pizzaballa, who is in charge of Franciscan monks in the region, was cited as the source of its information.
"The village had been under attack from Islamist rebels for the past few weeks, forcing the majority of the population to flee," the Vatican statement said. "When Father Francois tried to oppose resistance to defend the nuns and other people, the guerrillas shot him, killing him."