Deleting abusive tweets soon after they are published may save offenders from prosecution.
Keir Starmer, director of public prosecutions, said it was "relevant" for police to consider whether an offending tweet had been quickly deleted from the micro-blogging site.
Speaking to Sky News' Dermot Murnaghan, he said he was holding a three-month consultation about the plan.
Libellous tweets, or messages which broke court orders or were threatening, would still face prosecution regardless, he added
Mr Starmer said: "There's a lot of stuff out there that is highly offensive that is put out on a spontaneous basis that is quite often taken down pretty quickly and the view is that those sort of remarks don't necessarily need to be prosecuted."