Sunni Muslim, Tanveer Ahmed, 32, from Bradford in Yorkshire, is serving a life term for stabbing Ahmadi Muslim, Asad Shah, 40, in Glasgow on 24 March.
He said the victim disrespected Islam by falsely claiming to be a prophet.
It has now emerged that messages, apparently recorded from Ahmed's phone calls from Barlinnie Prison, have been posted on the video-sharing site.
Why was Asad Shah murdered?
The audio, which appears to be a landline phone call, is presented with a still picture of the killer.
The messages, in Urdu, include phrases such as "we should all try to make the world a better place" and "I will sacrifice myself".
The Scottish Prison Service has made no comment although it is known phone calls from prisons are monitored.
Police Scotland said it was aware of the communications and was assessing the situation.
The development emerged on the same day Ahmed was given leave to appeal his 27-year minimum jail term.
In July, he 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.
In return for guilty pleas, Scottish judges have the discretion to reduce sentences by as much as 30%.
When Ahmed was convicted, judge Lady Rae said that if he had not admitted the crime, she would have sentenced him to 30 years in jail.
Ahmed's legal team argue that the sentence was excessive and he should have been given a larger discount.
A judge rejected that ground for appeal earlier this year.
But following a short hearing in Edinburgh on Thursday, judges Lady Dorrian, Lady Clark and Lord Menzies allowed it to be reinstated.
It will now be a second point in Ahmed's appeal against sentence.
The first appeal point is that trial judge Lady Rae's belief, that the crime would have merited a 30-year jail term, is incorrect and excessive.
Lady Dorrian said: "We are content for the two points to proceed together."
The date of Ahmed's appeal is yet to be fixed. He was represented by Brian McConnachie QC and was not present in court.
Ahmed drove from his home in Bradford to kill Mr Shah and attacked him at his store in Glasgow's Shawlands area.
Police are investigating how phone messages from a religiously-motivated murderer ended up on Youtube.