Five foreign cadets based at Bassingbourn Barracks, near Cambridge, were jailed last year for attacks in the city committed in 2014.
They were based in the UK as part of a British Government agreement to train Libyan troops.
The MoD confirmed it was considering compensation claims.
The first claimant is understood to be the male victim of Moktar Ali Saad Mahmoud, 33, and Ibrahim Abugtila, 23.
They were both jailed for 12 years for rape after a court heard they acted like "hunting dogs" as they sexually assaulted him in central Cambridge in October 2014.
Mahmoud and Abugtila denied attacking the man, who had earlier been at a wedding, but were caught on CCTV leading him to the park.
At least one more claim has been submitted by one of three women assaulted on the same night in separate attacks.
Khaled El Azibi, 19, Naji El Maarfi, 21, and Mohammed Abdalsalam, 28, were jailed after they admitted a range of charges relating to the female victims.
Their attacks included trying to kiss a woman without consent and then sexually assaulting her.
It is understood one victim is making her claim on the basis of negligence and breach of human rights
In the aftermath, the MoD sent 300 soldiers back to Libya early, ending an agreement to put 2,000 soldiers through basic infantry and junior command training.
An MoD spokeswoman said: "We can confirm that compensation claims have been received by the department.
"As the claims are ongoing we are unable to comment further."
The Ministry of Defence (MoD) has received legal claims from victims raped and sexually assaulted by Libyan soldiers training in the UK.