Miliband said: "We have noted the remarks by Ayatollah Jannati suggesting that some of our local staff in Iran may face trial."
"We are urgently seeking clarification from the appropriate Iranian authorities. I intend to speak to Iranian Foreign Minister Manouchehr Mottaki," the foreign secretary said.
"We are confident that our staff have not engaged in any improper or illegal behavior. We remain deeply concerned about the two members of our staff who remain in detention in Iran," he said.
Earlier media reports said that nine local staff of the British embassy in Iran had been arrested for their alleged "considerable role" in the post-election riots.
The British government said that two of the nine staff were still in detention.
Iran has repeatedly accused foreign powers, especially Britain and the United States, of stoking unrest in the country after the June 12 presidential election, which handed incumbent President Mahmoud Ahmadinejad a decisive victory.
The European Union on Friday summoned Iranian ambassadors in protest against the detention of British embassy staff in Tehran.