Mr Shakuri is believed to have been implicated in attacks on coalition troops by Iraqi militias armed and supplied by Iran.
One official said he had a record of acting as the field officer in foreign-based terrorist activities carried out by the Islamic state.
America had sought British involvement after it became clear that Mr Shakuri was active in providing materials to make roadside bombs and other explosive devices in southern Iraq. He is also believed to be linked to attacks in Kerbala carried out by a group that kidnapped five British men in Iraq, killing four of them.
"This is something that Britain has been aware of for some time and we have been working to help the American investigation," a British official said.
While officials have been unable to confirm his whereabouts, there were concerns last night that he had been able to reach sanctuary in Iran. Mr Shakuri was a key lieutenant of Alireza Shahlai, a senior commander in Iran's Revolutionary Guards' Quds Force and a cousin of the other plot suspect, Manssor Arbabsiar.
Officials believe it was Shahlai, who is subject to US treasury sanctions for terrorist activities in Iraq, who masterminded the plot, which was to have involved a bomb made from plastic explosives.
It has been claimed that after his arrest in Texas, Mr Arbabsiar made several calls to Mr Shakuri.