One family has already described the offer as an insult.
Negotiations between the ministry and families have been going on for months, in the wake of David Cameron's 2010 apology and declaration that the shootings by paratroops were "unjustified and unjustifiable".
Paratroopers opened fire on innocent civil rights marchers in Londonderry in 1972.
Kate Nash, whose brother William was killed and father Alex injured, said: "My brother cannot be replaced and all the money in the world won't bring him back."
Her father, Alexander Nash, saw his son William, 19, being shot by members of the Parachute Regiment in the Bogside area on Bloody Sunday on 30 January 1972 and went to help him. He was then shot and wounded himself.
Ms Nash said she was simply interested in accountability and not money.
"I became slightly outraged at that. How do they pick out the seriously injured? My father recovered, he was shot through the arm and the side. My father was in a bunker watching his son die.
"How in terms of compensation could you ever make up for that?"
She added: "My father was not just physically seriously injured, he was mentally seriously injured."
He died in January 1999.
The Saville Report into Bloody Sunday was published in June 2010, prompting Prime Minister David Cameron to apologise to the families and describe the killings as "unjustified and unjustifiable".
The massive document, which took 12 years to complete at a cost of £195 million, was heavily critical of the Army and found that soldiers killed people without justification.
The report concluded that none of the victims were armed, that soldiers gave no warnings before opening fire and that the shootings were a "catastrophe" for Northern Ireland, leading to increased violence in subsequent years.
Police in Northern Ireland last year said they will launch a major investigation into the deaths.
The experience of the Bloody Sunday families will be closely watched by campaigners for justice for other atrocities.
Traditional Unionist Voice leader Jim Allister expressed outrage at the proposed compensation.
"After the millions already spent on inquires and investigations into Bloody Sunday, this is another handout from the British taxpayer," he said.
"A multitude of victims have never had a single penny spent on any inquiry investigating the murder of their loved ones, much less a cheque for £50,000."
Belfast-based law firm Madden and Finucane represents many of the Bloody Sunday relatives.
A spokesman said: "Negotiations in respect of compensation are continuing with the Ministry of Defence and their legal representatives.
"The contents of those negotiations shall remain confidential between the families of those murdered and the wounded whom we represent and the MoD."