The High Court is due to hear arguments today (Friday 10 June) about whether to grant an injunction to stop the first planned flights from sending asylum seekers to Rwanda.
It has been reported campaign groups are trying to bring about the legal action.
The Public and Commercial Services Union (PCS), Care4Calais and Detention Action have issued judicial review proceedings in the High Court, challenging what they describe as an "unlawful policy" by Home Secretary Priti Patel to remove asylum seekers to the east African nation.
The Home Office says it wants to stop the trade of smugglers transporting people across the Channel.
More than 10,000 migrants have crossed the Channel to the UK so far this year arriving in Dover, Kent.
The first flight from the UK containing migrants is expected to leave on Tuesday next week.
However, lawyers for more than 90 migrants have already submitted legal challenges asking to stay in the UK.
Clare Moseley, founder of Care4Calais, said the vast majority of the 100 or so people being detained pending their removal to Rwanda that lawyers have spoken to are "overwhelmed by total shock and despair".
She said: "Many came to the UK believing it to be a good place that would treat them more fairly than the places from which they escaped.
"We say that the Rwanda plan is unlawful. We hope the courts will agree with us."
A Home Office spokeswoman said: "Our world-leading partnership with Rwanda is a key part of our strategy to overhaul the broken asylum system.
"We have been clear from the start that we expected legal challenges however we are determined to deliver this new partnership.
"We have now issued formal directions to the first group of people due to be relocated to Rwanda later this month. This marks a critical step towards operationalising the policy, which fully complies with international and national law."