Fewer than 10 migrants could be deported on the first flight to Rwanda as a result of legal complications.
Home Office officials fear the number could be in single figures due to legal challenges on behalf of migrants.
Hundreds of migrants have already been detained in the past two weeks ready for the first flight scheduled for the end of June or beginning of July.
The initial cohort of 5,700 migrants have already been earmarked for deportation.
Rwanda deportation flights have previously been blocked by the ECHRPAA source close to the planning of the flights told The Times: "We will do well to get to double figures on the first flight because of the attrition rate due to legal challenges."
Claims can be lodged by migrants set to be deported to the African country if they can provide "compelling evidence relating specifically to the person’s particular circumstances."
Legal challenges are expected to be based on articles two and three of the European Convention on Human Rights (ECHR), which protect the right to life and guard against torture.
The first flight scheduled to depart for Rwanda in 2022 had just seven migrants on board before it was blocked by European judges.
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Former Home Secretary, Suella Braverman, visiting the potential migrant housing estate in Kigali, RwandaPAHowever, the claim that the upcoming flight would have a small number of deportees on board is being disputed by official sources.
A Home Office spokesman told The Times: "The deterrent within the Rwanda policy is simple and already showing signs of working.
"If you come to the UK illegally, and now if you are a failed asylum seeker with no right to be here, you will be removed. That was always the aim and is neither new nor rushed."
"We do not recognise these claims and they do not reflect our current operational planning. Detentions for those in line for removal are continuing and we are working at pace to get flights off the ground in July."
It comes as the EU is facing demands from more than half of its member states to allow them to control their own migration policies, with several asking for the right to introduce their own Rwanda-style deportation schemes.
The revolt is being led by Italy and the Czech Republic.
Czech Prime Minister Petr Fiala said: "The Czech Republic and Italy are among the countries that want to go beyond where the migration pact has taken us and want to find a real solution to illegal migration, which we do not yet have in Europe."