The First Minister revealed for the first time yesterday that his confidential financial records were allegedly targeted in 1999, as he denied there was any evidence that his phone had been hacked.
Mr Salmond, whose claims made under oath to the Leveson Inquiry into press standards relate to the Observer, said he was convinced that illegal activity was "rife" in the newspaper industry.
However, last night, the publisher of the Observer said it had been unable to find "any evidence to substantiate" his allegations.
In a letter to Mr Salmond last year, the paper's managing editor also said the matter could not go any further unless the SNP leader named his source.
But sources close to the First Minister confirmed he had refused that request, insisting the paper had a duty to investigate allegations of criminal behaviour.
Mr Salmond said he had been told by a former Observer reporter that his bank account was targeted in the run-up to the 1999 Scottish elections, when he was the SNP leader. He said he had been told the paper knew details of recent transactions, information he said could only have come from his confidential records.
He added: "For example, I bought some toys for my then young nieces in a toy shop in Linlithgow High Street which was called 'Fun and Games'.
"The person who informed me told me this caused great anticipation and hope in the Observer investigation unit because they believed that perhaps 'Fun and Games' was more than a conventional toy shop."
The revelations came as former Sun editor Rebekah Brooks, 44, and her husband Charlie, 49, were yesterday bailed at Southwark Crown Court ahead of a trial, accused of conspiracy to pervert the course of justice.
Culture Secretary Jeremy Hunt also narrowly survived a Commons vote after LibDem Deputy Prime Minister Nick Clegg called for him to face an inquiry following his evidence to Leveson.
Prime Minister David Cameron has been prepped by a senior government lawyer ahead of his appearance later today at the inquiry he set up in the wake of the phone-hacking scandal.
SNP sources last night said the First Minister had also been told of a number of other specific examples which had convinced him that the paper had obtained details about his account.
It is not the first time the newspaper has faced questions over its working practices. An investigation into the press by the Information Commissioner in 2006 detailed more than 100 instances where it was thought the Sunday title had obtained information "illegally".
The Observer is part of the Guardian News & Media group. It also publishes the Guardian, which revealed in July last year that murder victim Millie Dowler's phone had been hacked by the News of the World, triggering the phone-hacking scandal that led to the tabloid's closure.
Mr Salmond also accused the Metropolitan Police of withholding evidence from Scottish authorities. The SNP leader said he had been assured by Strathclyde Police that those responsible would face court.
He also denied doing a deal with the Murdoch empire to back its BSkyB deal in order to secure the support of the Sun newspaper. Mr Salmond said he had agreed to argue on behalf of the bid because he thought it would be good for jobs in Scotland.
He had been under intense pressure from opposition parties to confirm whether he had been a victim of phone-hacking during his appearance.
He said he had no evidence that his own phone was targeted and that he understood Strathclyde Police had finished informing potential victims.
A spokesman for Guardian News & Media said that Mr Salmond first raised the allegations last summer.
He added: "As we explained to him [Mr Salmond] last year, on the basis of the information he had given us, we have been unable to find any evidence to substantiate his allegation.
"As our response to him at the time made clear, we take this allegation very seriously, and if he is able to provide us with any more information we will investigate further."