The 19-year-old French native murdered the priest on July 26th
Community leaders in Saint-Etienne-du-Rouvray said they did not want to "taint" Islam by having any association with Adel Kermiche, the 19-year-old jihadist who killed Fr Jacques Hamel in his hometown in northern France.
Mohammed Karabila, president of the local Muslim cultural association and imam of one of the town's mosques, told Le Parisien: "We're not going to taint Islam with this person.
"We won't participate in preparing the body or the burial."
Muslims in the town were supportive of the decision.
Khalid El Amrani, a 25-year-old technician, said he thought it was "normal" that the mosque would refuse to help with the burial.
"What this young man did was sinful, he is no longer part of our community," he said.
The mayor's office will have the final say on whether Kermiche can be buried in the town.
Kermiche and Abdel-Malik Petitjean, also 19, stormed into the 17th-century stone church on 26 July, taking hostages before killing the priest and seriously wounding another captive.
They were shot dead by police as they exited the building using nuns as human shields.
The two nuns who were in the church when Fr Jacques Hamel had his throat cut said one smiled as he carried out the attack.
Sister Huguette Peron told Catholic newspaper La Vie: "I got a smile from the second (man). Not a smile of triumph, but a soft smile, that of someone who is happy."
At one point, Sister Helene got tired and asked to sit down.
She said: "I asked for my cane, he gave it to me."
Then the men started talking about religion, asking the nun if she was familiar with the Koran.
"Yes, I respect it like I respect the Bible, I've read several suras. And those that hit me in particular are the suras about peace," Sister Helene responded.
One of the attackers replied: "Peace, it's what we want ... as long as there are bombs on Syria, we will continue our attacks. And they will happen every day. When you stop, we will stop."
Meanwhile, the adoptive father of Abdel Malik Petitjean told how news of his son's crime and violent death had left him "broken".
Franck Petitjean said: "I haven't slept in days. In three months they (IS) brainwashed him."
He said he feared his daughter would want revenge for her brother's death and could be lead down the same path.
Police are still interviewing three people and a 19-year-old man has been charged with terrorism offences as authorities try to track down accomplices of the two attackers.