Lakhvir Singh and Sumit Sehdev were released from Border Force detention after crowds swarmed around the van in which they were held.
Demonstrators blocked the vehicle from leaving the Pollokshields area of the city for several hours on Thursday with one even lying underneath its axles. Officials eventually released the pair on public safety grounds.
Now charity Positive Action in Housing has said it is investigating the possibility of bringing action against the government.
Director Robina Qureshi said: “The Home Office have referred to these men as illegal. Well they are wrong, and we are now investigating legal action against the Home Office for casting such aspersions.
“The term ‘illegal’ in this context is part of the hostile environment. It’s not appropriate to use it for people who have lived in the UK for several years and are part of a community.”
Mr Singh and Mr Sehdev, both in their thirties and reportedly a mechanic and chef respectively, have become much respected members of the local community, he added.
And he said: “Dawn raid vans have no place going into communities dragging innocent people from their homes. They are not, categorically not, criminals.”
The Home Office has not yet responded to the development but on Thursday a spokesperson said: “The UK government is tackling illegal immigration and the harm it causes, often to the most vulnerable people, by removing those with no right to be in the UK.
“The operation in Glasgow was conducted in relation to suspected immigration offences and the two Indian nationals complied with officers at all times.
“The UK government continues to tackle illegal migration in all its forms and our New Plan for Immigration will speed up the removal of those who have entered the UK illegally.”
Scottish justice secretary Humza Yousaf has called the detention’s a “reckless action”, while the first minister Nicola Sturgeon has attacked what she calls the UK government’s “appalling asylum and immigration policy”.