The campaign, which is expected to focus on regional print and direct marketing, will aim to educate consumers about what constitutes antisocial behaviour and how they can tackle it by reporting it to the relevant authorities.
Fallon, Euro RSCG London and M&C Saatchi are pitching for the brief, which is being overseen by COI Communications. COI is not looking to appoint an agency to handle media planning.
Both Euro RSCG and M&C Saatchi have created work for the Home Office in the past. Euro RSCG created a campaign to combat gun crime; while M&C Saatchi is responsible for the "Could you?" police recruitment campaign.
However, Fallon, which was added to the roster in 2001, has yet to create any work.
The antisocial behaviour campaign is part of an effort by the Government to reduce low-level crime such as vandalism, begging and nuisance neighbours.
In January, the Government launched its "together" initiative, which targets the police, local authorities and housing and environment officers to encourage them to help drive down this kind of crime.
A Home Office spokesman confirmed it is talking to agencies, but did not give further information about the pitch.