Khaled El Azibi, Naji El Maarfi and Mohammed Abdalsalam carried out the attacks while stationed at last October.
The men's victims are due to receive letters informing them of the "unacceptable" situation, solicitor Richard Scorer of Slater and Gordon said.
He added: "These men were invited here as guests, to this country, to be trained and to provide help for them in their home country.
"They abused that hospitality in the most appalling way imaginable, and the idea that they would then be granted asylum - having committed these crimes - is completely wrong and unacceptable.
"It adds insult to injury for the women concerned. What we are saying is that it would be completely unacceptable and completely wrong if they were to be granted asylum. I would think that most people would regard it as completely unacceptable that they should be allowed to remain in this country any longer."
Accosted three teenagers
A Cambridgeshire Police spokesman said: "All three men have been released from prison into secure immigration units and are now seeking asylum."
The cadets were among 300 troops being trained to support the newly-formed Libyan government.
They stole bicycles and rode into Cambridge city centre before accosting three teenage women during the early hours of October 26 2014.
The attacks included trying to kiss a woman without consent and then sexually assaulting her. El Maarfi exposed himself to one of the women.
Each of the men served between 10 and 12 months in jail before being released from prison.
Two other cadets were jailed for a brutal rape in a separate incident on the same night last year.
Moktar Ali Saad Mahmoud, 33, and Ibrahim Abugtila, 23, were both jailed for 12 years after acting like "hunting dogs" as they raped a man.
Collapse of discipline
The attacks were part of other concerning conduct by Libyan cadets at the base following a "collapse of discipline".
The incidents prompted the Ministry of Defence to send the soldiers back to their home country early, ending an agreement to put 2,000 soldiers through basic infantry and junior command training in an attempt to help rebuild the troubled nation.
Prime Minister David Cameron previously insisted that no Libyan soldiers involved in the programme should be granted asylum after a "very small handful" made applications to stay in the UK.
Defence Secretary Michael Fallon said that, of the 328 total originally signed up to the scheme, around 100 left during the course of their training by agreement with the Libyan authorities.
The remainder have all been returned "properly" to Libya, he added, apart from the five convicted of sex offences and those others and those who had applied for asylum.