Banning radical Islamists from working unsupervised with children could be one measure included in a new government anti-extremism strategy, reports say.
The Sunday Telegraph says it has seen a leak of a draft Home Office document, which also suggests Sharia courts and councils are areas of concern.
Job centre staff may be required to identify vulnerable claimants who could become targets for radicalisation.
The BBC understands the document has yet to be signed off by the coalition.
A Home Office spokesman said the government did not comment on leaked documents.
A new government strategy on tackling extremism has been working its way through Whitehall for some time.
The document proposes a number of new measures, including tightening the rules on citizenship to make sure new residents embrace “British values”.
It says the government needs to be “more assertive” in challenging extremists who oppose democratic values.
The Telegraph quotes the document as saying: “In the past, there has been a risk that the government sends an ambivalent and dangerous message – that it doesn’t really matter if you don’t believe in democracy.
“We need to stand up and be more assertive in promoting our values and challenging the extremists who fundamentally oppose them.
“This will include explaining our foreign policy [and] promoting mainstream voices supporting the quiet majority in all communities who oppose extremism.”
BBC political correspondent Ben Wright says the coalition parties still need to approve the document, but in principle there is nothing to stop measures being introduced immediately, although there is very little time before the election.
He adds that the question of how to prevent extremism in Britain is again acute.
It comes in the wake of three British schoolgirls travelling to Syria, apparently to join Islamic State, and IS fighter “Jihadi John” being identified as Mohammed Emwazi, who was educated in west London.
Police cuts warning
Meanwhile, the retiring president of the Association of Chief Police Officers (Acpo) has warned that further cuts to policing in Britain could leave forces without the resources to protect the public from threats including terrorism.
Sir Hugh Orde told the Observer newspaper that taking police off the streets was a clear risk in the fight against extremism.
He said: “The critical element, it seems to me, with dealing with people who will start to behave differently in their communities is the confidence in that community to speak to the local cops.
“If the cops aren’t there, and that relationship has not been built, we won’t get the intelligence.”