Making it prescriptive for media outlets to contact the subjects of stories involving privacy issues before publication 'could be worse than the problem', Straw told a House of Commons select committee hearing on press standards, privacy and libel.
In a previous committee hearing Max Mosley suggested that prior notification should be a legal requirement for media organisations; while media commentator Roy Greenslade said he did not wish to see this introduced.
Straw said he was 'sceptical' about making it law, despite having been contacted by the Telegraph himself prior to publication of a recent expenses story, which was found to be untrue.
It is in the interests of news organisations to be accurate and newspapers should be able to judge for themselves whether prior notification is necessary, said Straw, citing the example of putting a witness at risk by notifying a criminal subject.
More use should be made of the Press Complaints Commission's (PCC) code if a subject feels they should have been notified, he said.
"My first port of call here would be the PCC code, with the understanding that if that was breached in a particular case then that breach of the code would be (...) drawn to the attention of a judge during proceedings," explained Straw.
Straw said it was not his role to comment on whether judgments made by Justice Eady were unduly shaping UK privacy law - as has been suggested by Daily Mail editor Paul Dacre.
Newspapers are 'getting gradually better' at not intruding into the lives of individuals who do not volunteer for public life, he said.
The issue of high case costs and conditional fee agreements for media organisations is of greater concern than reviewing prior notification procedures, he added.
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