The kill mission is part of renewed efforts to eliminate Islamic State commanders in Syria and will happen regardless of the outcome of Wednesday's vote in parliament, the Daily Express reported.
Sally Jones, a mother of two from Kent, who has made herself invaluable to the Islamic State of Iraq and Syria (ISIS) is believed to be among the targets.
Jones' husband Junaid Hussain was killed in a drone strike in the ISIS "capital" of Raqqa, Syria - the same city where the US also caught up with "Jihadi John" - in August.
Around 40 members of the SAS are already supporting US Special Forces in Syria but that number is to be doubled after defence chiefs ordered the head of Britain's special forces to focus all efforts against ISIS jihadis in Iraq and Syria.
Though the force will take part in a range of missions, its main task will be to target key British extremists.
A vital part of ISIS' recruiting machine, she has vowed to behead Christians.
According to intelligence sources, her links with the UK make her a "live threat" to national security.
In total 10 Britons are believed to be on the list, including British brothers Nasser and Aseel Muthana, aged 20 and 17.
They left for Syria last year and are believed to have been close associates of the two Britons killed in the August drone strike. In all, more than 700 British nationals have left the UK to join ISIS.
The kill list was created from intelligence supplied by GCHQ, the government's eavesdropping service, and the US National Security Agency.
Both organisations have spent the past two years monitoring phone calls and internet activity between terrorists.
British Special Forces have already formed a series of "hunter-killer" teams with US counterparts, including Delta Force and Seal Team 6.
