Sunni Muslim, Tanveer Ahmed, 32, from Bradford in Yorkshire, stabbed 40-year-old Asad Shah outside his store in Glasgow's Shawlands area on 24 March.
Mr Shah was an Ahmadi - a minority sect not recognised by all Muslims.
Ahmed admitted the murder and said the victim had disrespected Islam by falsely claiming to be a prophet.
Why was Asad Shah murdered?
In July, Ahmed pleaded guilty to the religiously-motivated murder at a hearing at the High Court in Glasgow.
Last month, he was given a mandatory life term and told he must serve a minimum of 27 years before he can apply for parole.
Jailing him, judge Lady Rae told Ahmed: "This was a barbaric, premeditated and wholly unjustified killing of a much-loved man who was a pillar of the local community.
"He was described as a peaceful and peace-loving man and family man who went out of his way to show respect for those of any faith."
The judge branded the attack as "an appalling display of merciless violence".
It has now emerged that lawyers for Ahmed have lodged an appeal against his sentence.
The court previously heard that Mr Shah was an Ahmadi,  who differ from the majority of Muslims, including Sunni Muslims, in that they believe the Prophet Muhammad was not the final prophet.
The majority of Muslims believe Muhammad was the final prophet and say any other view is inconsistent with Islamic belief.
Ahmed, a Sunni, claimed that he had killed Mr Shah because he had posted videos online in which the shopkeeper had "disrespected" Islam by claiming to be a prophet.
Ahmed watched a clip featuring Mr Shah on his mobile phone as he travelled to Glasgow on the day of the murder and was heard in a phone message to say "listen to this guy, something needs to be done, it needs nipped in the bud".
When he arrived at the shop, Ahmed said he warned Mr Shah that he was there to kill him and asked him to stop claiming to be a prophet.
CCTV footage of the attack showed Ahmed pulling a knife out and moving behind the counter and stabbing Mr Shah repeatedly.
The shopkeeper managed to get outside, but was stabbed again and then stamped on and kicked in a frenzied attack as he lay dying in the street.
Mr Shah's brother Athar Shah tried to intervene, but was unable to fend off Ahmed.
As Mr Shah lay dying on the ground, Ahmed walked calmly to a bus shelter where police found him a short time later.
After being arrested, Ahmed released a statement through his lawyer saying he had killed Mr Shah as he had falsely claimed to be a prophet.

Crowd favourite Molinari and England's Willett began the day level on 16 under par, but the Italian hit a round of 65 to edge home in a thrilling finale.
Spain's Nacho Elvira finished four shots back on 18 under par, tied for third with England's Chris Paisley.
Fellow Englishmen David Horsey, Richard Bland tied for fifth on 15 under.
Tommy Fleetwood and Scotland's Scott Jamieson were among five players tied for seventh.
Molinari, 33, hit one eagle and five birdies in Sunday's final round to become the first Italian to win his national Open twice since the event became part of the European Tour in 1972.
The victory was the Italian's fourth at a European Tour event and a first since the Reale Seguros Open de Espana in 2012.
Seven of the European Ryder Cup team, which includes Willett, were competing in Monza as they prepare to take on the United States at Hazeltine in Minnesota from 30 September to 2 October.
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A man who was jailed for life for murdering a shopkeeper who he claimed had "disrespected" Islam is to appeal against his minimum 27-year jail term.
[NEXT_CONCEPT]
Francesco Molinari carded a six-under-par final round to beat Masters champion Danny Willett to the Italian Open title by a single shot in Monza.