A five-person panel of legal experts and journalists was appointed in December to consider the recommendations of the Leveson Report into press standards.
It was chaired by Lord McCluskey, senator of the College Of Justice and a former Solicitor-general, with a view for the panel to assess reforms to the Scottish press under Scots Law and make recommendations to the Scottish Government.
News of the reforms report came hours after First Minister Alex Salmond held a cross-party meeting with the Scottish Newspaper Society.
A Scottish Government spokesman said: "The meeting gave all of the main party leaders in Scotland the opportunity to listen to the views of the press in Scotland as the Scottish Parliament prepares to respond to the recommendations made by Leveson.
"The report by the expert group, led by Lord McCluskey on how the Leveson recommendations could be applied in the Scottish context, is expected to be published on Friday and we will continue discussions with other parties on the next steps."
The publication of the Scottish document will come the day after Prime Minister David Cameron decided to dodge cross-party consensus on press regulation at Westminster. He will force a vote on the issue in the Commons on Monday.
Mr Cameron said he would publish a Royal Charter to underpin a new self-regulatory system for the press without the need for Parliamentary legislation.
His amendment to the Crime And Courts Bill will not provide statutory underpinning for the new regulator, but will allow courts to impose "exemplary damages" on newspapers that refuse to join the system.
Labour is expected to publish its own amendment later today.