More than 1,350 women have inquired about joining the Commandos, according to a Sunday Times report.
It comes two years after then-Prime Minister David Cameron announced that the ban on women serving in “ground close” combat roles would be lifted.
More than 1,350 females have inquired about becoming potential bootnecks, and 20 have gone on to begin the selection process, the Sunday Times reports.
The newspaper said it understands they are undergoing preliminary testing, which involves an interview and two one-and-a-half mile timed treadmill runs.
A Royal Navy spokesman said:
“Last year a number of female recruits who had expressed an interest visited CTC Lympstone for a familiarisation visit.”
The women have been told they must meet the same physical standards as men, and will sleep in the same dormitories to protect “troop cohesion”. However, female recruits will be provided with separate toilets and showers with lockable doors.
To achieve the coveted green beret, recruits must complete a nine-mile speed march in 90 minutes, and a six-mile endurance course in under 73 minutes, and 71 minutes for officers.
An aerial assault course must also be finished in under 13 minutes, and 12 minutes for officers, as well as a 30-mile march across Dartmoor while carrying equipment and a rifle in eight hours, and seven for officers.
The move to relax the rules came in July 2016 after extensive research, and a recommendation from the then-head of the British Army, General Sir Nick Carter.
At the time, the Ministry of Defence (MoD) said it would adopt a phased approach, starting with the Royal Armoured Corps (RAC), which would then be followed by the infantry, the Royal Marines and the RAF Regiment.
Earlier this year it was reported that one female RAF Regiment recruit quit two weeks into an 18-week course after falling behind her male counterparts.
The decision to lift the ban saw the UK join Israel, Australia and the United States as among countries which allow women to serve on the front line.