David Norris and Gary Dobson are likely to be given extra protection in prison to prevent them from being attacked by fellow inmates.
The racist killers could be held on wings reserved for “vulnerable” prisoners such as paedophiles and kept away from other prisoners.
Fears over their safety were raised after Norris was attacked by Asian inmates while on remand at Belmarsh prison in south east London, England.
His nose was broken, he lost a number of teeth and suffered four broken ribs in the attack in February.
Norris had to use a hearing device to be able to listen to evidence.
He and Dobson were taken from the Old Bailey back to Belmarsh prison earlier today and could be transferred to other category A prisons in the near future.
But prison staff could put measures in place for their safety if it is thought there is a clear risk to their safety.
Other prisoners, including Soham murderer Ian Huntley, have claimed compensation after being injured by inmates.
The killer of schoolgirls Holly Wells and Jessica Chapman made the £100,000 claim, saying the prison service failed in their duty of care towards him, after he had his throat slashed in March 2010.
Figures released by the Ministry of Justice last year showed inmates were paid more than £10 million in compensation over the last five financial years for harm caused while behind bars.
Two payments to prisoners of more than £100,000 were made in 2010/11 alone as part of almost £1.6 million in settled claims, figures released to the Press Association under freedom of information laws showed.
The highest payout last year was £125,000, followed by payments of £100,000, £95,000 and £62,867 – all for personal injury cases.