The Home Office is in talks with lawyers over plans to toughen up the law on stalkers.
It is understood the discussions are centring on examples of specific anti-stalking laws in the US, Canada and Australia.
In a letter to The Independent earlier this month, Home Office Minister Timothy Kirkhope said: "There are real difficulties in extending the law without criminalising routine and essentially harmless behaviour, but we are not complacent. We want to offer as much protection as possible to the victims of this abhorrent behaviour."
The Law Society's criminal law committee secretary Roger Ede has warned any legislation would have to be carefully drafted so people are not convicted of a criminal offence when their behaviour has not warranted a serious penalty.
However, he welcomed the move to clamp down on the problem of stalking.
The police currently rely on the Criminal Justice Act 1994 in harassment cases.