Senior police officers and government ministers could be brought before a Holyrood committee to answer questions over spying allegations.
Scottish Liberal Democrat justice spokesperson and Policing Sub-Committee member Alison McInnes MSP has written to Convener Christine Grahame to ask that the parliamentary committee investigate the claims.
If agreed, an inquiry could result in senior figures from Police Scotland and the Scottish Government being asked to provide evidence.
It emerged last month that two un-named UK police forces had been involved in spying on journalists and their sources.
The Sunday Herald newspaper claimed that Police Scotland is one of those forces and yesterday an investigative journalist told BBC Scotland he believed the national force may have monitored his communications illegally.
In a letter to the Policing Sub-Committee Convenor, Ms McInnes said: “Reports that Police Scotland has been involved in illegally spying on journalists threaten to sour public trust in our public institutions.
"The refusal of the national force and Scottish Government to confirm or deny Police Scotland’s involvement in this matter will only fuel concerns about a conspiracy of silence.
"I am writing to ask that the Policing Sub-Committee undertake a full inquiry into these allegations in order to ascertain Police Scotland’s involvement. This would allow both ministers and Police Scotland bosses to set the record straight.
"Our police officers play a vital role in keeping us safe but I am sure that you will agree that they are not above the law.
"The rules around accessing communications data were changed under the last UK government for good reason.
"A free press is vital to holding the powerful to account. It is the duty of parliament to hold those in public office to account.”
Police Scotland says it would be inappropriate to comment at this stage, while the Scottish Government says obtaining communications data is a matter reserved to the UK Parliament and the IOCCO.