The First Minister repeated his insistence a new regulator must be underpinned by statute following Lord Justice Leveson's report on the behaviour of the press. But, in a bid to build cross-party support, he indicated a UK-wide body, created by the newspaper industry, could fulfil criteria for handling complaints and monitoring practices.
He said a judge, rather than a Government minister or quango, could be given the final say on whether the proposed new regulator met the criteria.
In his response last week Mr Salmond proposed a legally recognised press council and ombudsman modelled on the Irish system. However, he has faced mounting pressure not to burden newspapers with a separate regulatory body.
Prime Minister David Cameron wants to avoid legislation and told newspaper publishers to devise a tough new watchdog.
Mr Salmond said: "It is up to the press, not the Government, to establish its own regulatory structure. Depending on what the press decides, that structure could apply to other parts of the United Kingdom."
But he stressed: "A Scottish solution is required for underpinning the self-regulatory body. Lord Justice Leveson's own view is surely unarguable.
"His recommendations require serious, expert and distinctive consideration within Scotland. They cannot just be left to Westminster."
It comes as 20 editors were summoned to Downing Street to discuss reforms, with the Prime Minister insisting they must devise a new independent regime of regulation if they want to avoid legislation to govern the industry.
Mr Salmond is due to meet opposition party leaders tomorrow for talks. He said he was optimistic about achieving cross-party support for his plan to set up an independent implementation panel led by a judge.
Scots LibDem leader Willie Rennie said: "It shows promise that the First Minister has conceded a UK-wide body is the most sensible way forward."
The LibDems and Labour have called for the Leveson proposals to be implemented across the UK. Under his scheme, a new regulatory body, devised by the industry, would be underpinned by law. However, it would face regular monitoring by broadcasting watchdog Ofcom.