The process is at the early stages and is being handled by the Central Office of Information (COI).
The DCSF has taken action after it emerged earlier this year that police receive more than 100 alerts per month from child internet users in danger of sexual abuse or violence on the internet.
Last week, it was reported that drifter Peter Chapman faces charges linked to the death of 17-year-old Ashleigh Hall, whom he allegedly met on the social networking site Facebook. Hall had told friends she had a date with a 16-year-old boy who had contacted her on the site.
A COI spokeswoman said: 'The DCSF is currently exploring what a public awareness campaign on internet safety might look like and we can confirm that the COI has issued a brief. It is, however, too early in the process to confirm any further details.'
Public sector comms specialists advised that any PR campaign would need to make use of a range of social networks to get the message across. Band & Brown public sector director Simon Francis said a PR campaign should target both parents and young people via popular online media and social networks.
'One of the most effective models for spreading this message would be through pre-existing networks and sources,' said Francis. 'Partnership marketing, not just with media, but with trusted brands, will be crucial.
'Yet also of vital importance would be the role of schools in instilling a sense of safety online from an early age. If internet safety is approached in a similar way to road safety, long-term benefits as well as short-term communications gains will be realised.'
Unity co-founder Nik Done said the key to reaching young people was to engage them through their own existing networks of friends.
'As with all campaigns aimed at a young audience, tone is everything,' said Done. 'We have run educational youth campaigns covering everything from teenage suicide to sun damage prevention. In every case we have gone to great lengths to avoid any kind of adult-to-child style of communication.
'Instead we have reached out to young people via young people, or by the people they aspire to be like. It's key that the communication feels both credible and relevant.'
HOW I SEE IT - Trevor Morris, Visiting professor for PR, University of Westminster
Changing behaviour is fantastically difficult. It is done over a considerable period of time and with the benefit of legal re-enforcement. Communications on its own would seldom do it.
Clearly, you need to reach parents, but the difficult thing is that parents are seldom internet-savvy enough to know what to do. It's very hard to control. Are you going to tell them to look at their kids' Facebook pages?
Part of growing up is growing up away from parents and learning to express yourself. And banning things can make them sexy to kids. It's an extremely hard brief.