The proposed law has been put forward by an official inquiry commissioned by the last government. It was presented to Justice Minister Beatrice Ask on Monday.
If the proposal becomes law, Sweden will have gone further than many other countries in legislating to protect children from sex attacks. A similar law has already been enacted in the UK, where grooming can lead to six months' imprisonment. If the contact leads to a physical attack, perpetrators face up to ten years in jail.
Grooming has become more common in recent years. The fast growing number of internet chat sites and communities makes it hard for police to stay ahead of the paedophiles.
Paedophiles are aided by the internet's anonymity. They can build up relationships with children and through manipulation try to bring about a meeting, which can lead to sexual attacks.
A report published on Monday by the Swedish National Council for Crime Prevention (Brottsförebyggande Rådet- Brå), showed the extent of the problem. In a survey of Swedish children aged 13-16, half the girls said that they had at some point been contacted by strangers whom they suspected to be adults and who had expressed a sexual interest.