Blogger Murray was sentenced to eight months in jail at the High Court in Edinburgh last month, relating to material capable of identifying four complainers in his coverage of the Alex Salmond trial.
The former ambassador to Uzbekistan watched two days of Mr Salmond’s trial in March last year from the public gallery of the court, writing about the case on his website.
During a hearing at the High Court on Monday, his lawyer Roddy Dunlop QC argued Murray should be granted permission to appeal to the UK’s highest court against the verdict of contempt of court and the sentence.
He said: “His submission is that imprisonment in a case such as this would be compliant with Article 10 (of the European Convention of Human Rights) only in exceptional circumstances. My submission is that that is not the case here.”
Mr Dunlop also argued that if the court were to find against his client, then Murray could still appeal directly to the Supreme Court.