Usually the Vatican has a five-year break between the death of a person and the launching of beatification process - the first step on the path to sainthood.
According to the Daily Telegraph, Vatican sources say the pontiff is preparing to make an exception for Fr Hamel.
Speaking at the Vatican last month the pope called the priest a "marytr".
Fr Jacques had his throat slit by two teenage extremists, Adel Kermirche and Abdel Malik Petitjean, both 19. The pair were shot dead by police.
His church in Saint-Etienne-du-Rouvray reopened on Sunday, more than two months after his murder.
