Britain's counter-extremism taskforce is working on the plans amid concern that preaching in foreign languages enforces divisions between Islam and mainstream British society and can foster radicalisation, according to The Sunday Telegraph.
"If imams are speaking in another language it makes it far harder to know if radicalisation is taking place," a government source told the newspaper.
The plans form part of the UK government's Prevent anti-extremism initiative, which will also be given a big increase in spending and staff.
Meanwhile, The Sunday Times reports the expansion of Prevent will go alongside a tougher approach to returnees from Islamic State (ISIS), with measures to exclude British citizens permanently from the UK.
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More than 30 dual nationals have been stripped of their British citizenship but the new drive could mean that many who hold only British passports are made stateless.
Ministers can cancel the citizenship of single-nationality Britons, if they were previously citizens of another country, and "temporarily exclude" British-born citizens from returning to the UK.
About 850 Britons are thought to have travelled to ISIS territory.
The UK Home Office said the strategy would be published "shortly" but refused to comment on what it called "speculation".