The Hillsborough Family Support Group insists it would be a "big mistake" to hold a minute's silence in tribute to Margaret Thatcher at football fixtures this weekend.
It comes ahead of Monday's 24th anniversary of the tragedy in which 96 Liverpool supporters were crushed on the terraces at Sheffield Wednesday's ground on April 15, 1989.
Reading, who entertain the Anfield club, confirmed on their website they will hold a minute's silence for the victims, as it was "absolutely correct to pay respect on such an occasion".
However, Reading chairman John Madejski had earlier joined Wigan counterpart Dave Whelan in supporting a tribute to Baroness Thatcher at the weekend's matches.
Neither the Premier League, the Football League nor the Football Association, which presides over Wigan's FA Cup semi-final against Millwall, have asked clubs to hold a minute's silence - or applause - in relation to the former prime minister, who died on Monday aged 87 after a stroke.
Margaret Aspinall, chairwoman of the Hillsborough Family Support Group, welcomed the decision to pay respects to those killed at Britain's deadliest stadium disaster.
But Mrs Aspinall, who lost her 18-year-old son, James, in the tragedy, said it would be a "mistake" to honour the former prime minister as well.
She said: "It's a terrible thing to speak ill of the dead, I know because it happened to my son and all the Hillsborough victims for 23 years.
"But if they do hold a minute's silence for Margaret Thatcher, I think they are making a big mistake.
"The fact is a lot of people would break that silence. Margaret Thatcher had contempt for football and its fans, in fact she was in favour of identity cards for all supporters."
In the hours and days which followed the disaster, the then prime minister held a number of meetings with police and other officials.
It remains a huge matter of concern for the families in their quest for answers that no notes or minutes were ever taken, or have survived if they were, during those meetings.
Mrs Aspinall said: "There are question marks because we don't know what role she played or what role her staff played, who said what to the prime minister, because nothing was written down, there were no notes, no minutes, nothing at all.
"It was soon after those meetings that the wicked lies appeared in the Sun.
"This weekend is about remembering 96 people who went to a football game one Saturday afternoon and, through no fault of their own, never came home."
Speaking to BBC Radio Five Live, Mr Madejski earlier said he would be in favour of a minute's silence for Baroness Thatcher.
"We have got to appreciate that Margaret Thatcher was a world leader who did so much for this country," he told the broadcaster.
"So much that she deserves a minute's silence.
"The funeral's going to take place at St Paul's (Cathedral), attended by the Queen and Prince Philip, so I think it would be a fitting tribute from the world of football to Margaret Thatcher, one of our greatest leaders."
He added: "No colossus like that strides the world's stage without disenfranchising people at some stage or another, however the positive things that Margaret Thatcher achieved for our country speak volumes and I think that outshines things that might not be considered so brilliant like the poll tax and so on."
Whelan also said he believed a symbolic gesture would be fitting.
"It is not my decision, it is for the FA to decide, but I would be in favour of wearing an armband out of respect to Mrs Thatcher," Whelan told BBC Sport.
"We have to say thank you very much for the services the former PM has given us."
Bob Crow, leader of the Rail, Maritime and Transport union and a keen Millwall fan, said: "It would be an absolute insult to the memory of the Hillsborough victims, and to all the millions of working people who suffered under Thatcher's regime, if there was a minute's silence at any football games this weekend, let alone the Wembley semi-finals.
"Wigan, and the North West, is one of the areas of the country that still bears the scars from the Thatcherite assault on jobs, services and Britain's industrial base.
"The idea that football supporters of all people are going to observe a tribute to a woman who connived with the lies against the 96 Liverpool fans who died in Sheffield is absolute madness."
Rugby club Saracens have however confirmed they will hold a minute's silence against Worcester Warriors.