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."

An online poll of more than 1,000 parents carried out by Mumsnet found that 18% of parents regretted the name they chose for their offspring, but only 2% actually changed their child's name.
The main reason for any regret was how regularly the name was used by others (25%), the data suggested.
Other sources of regret included spelling or pronunciation issues (11%).
The Mumsnet survey has been released in anticipation of annual statistics from the Office of National Statistics on the most popular baby names of the year in England and Wales.
Justine Roberts, founder of the parents' forum Mumsnet, said: "Choosing your baby's name is one of the first things new parents do, so in some ways baby name regret is great practice for parenting - you do a lot of hard work and research, try to please several people at once, and end up getting it wrong.
"The consolation is that most children grow into their names, and those who don't can always fall back on middle names, nicknames or, in extremis, deed polls."
According to the survey one mother said the moment she began to regret naming her daughter Elsa was when the Disney film Frozen became popular.
Another mum said: "My child hates his name, and makes me feel bad for choosing it."
While another parent admitted her child's name "was taken by a terrorist group, soon after she was born".
Last year Oliver and Amelia were revealed as the most popular baby names in England and Wales, while in Scotland it was Emily and Jack.
The Ministry of Defence (MoD) has received legal claims from victims raped and sexually assaulted by Libyan soldiers training in the UK.
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Almost a fifth of parents in the UK regret the name they chose for their child, a survey has suggested.