Speaking on Radio 4's Law in Action yesterday, Dominic Grieve QC said he is going to "mull over" the consideration and make a decision.
Grieve blamed what he called a "ritual of frenzied interest" after an arrest but before a suspect is charged, when reporting restrictions apply.
"It then disappears completely before there is a backlash, usually from the broadsheets. My desire is to inject a little bit of common sense into this."
Grieve cited the case of Chris Jefferies, the landlord questioned but released without charge in the case of Joanna Yates, whose body was discovered near Bristol on Christmas Day. The Independent said last month that it supported tighter reporting restrictions.
Veteran crime correspondent for the Times Stewart Tendler, who joined Grieve on the programme, agreed that reporting after an arrest but before someone is charged, with the press having been much more cautious prior to the 1970s. Tendler said a view that the media rushes to get as much detail out knowing "that the shutters will come down" when someone is charged. "The law has been stretched and pulled," Tendler said.
The Sun and the Daily Mail were recently found guilty of contempt of court after publishing a photograph online of a suspect in a murder trial carrying a handgun.
The jury had been told not to research on the internet but it was argued that the jurors could have seen the images as part of their daily news consumption as it was a picture used to illustrate the daily court report. Jurors did not see the picture and the trial was allowed to continue.
Law in Action presenter Joshua Rozenberg said some attorney generals have been "afraid of the power of the media" and have been cautious about taking out cases against news providers.
Grieve, who lead the case against the Sun and Daily Mail, urged the media to remember the contempt of court act, warning: "I won't hesitate to prosecute".
Image by Steve Punter on Flickr. Some rights reserved.