Wigan chairman Dave Whelan has called for a minute's silence ahead of Saturday's FA Cup semi-final against Millwall to mark the death of former UK Prime Minister Margaret Thatcher.
Baroness Thatcher, who led the country between 1979 and 1990, died in London on Monday at the age of 87 after suffering a stroke.
The Premier League and Football League will not be asking clubs to hold tributes at their forthcoming fixtures, and it is understood that the Football Association has no plans to mark her death either.
But Whelan, 76, told BBC Sport: "We owe Mrs Thatcher a minute's silence. 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.
"We have to say thank you very much for the services the former PM has given us."
Baroness Thatcher alienated football fans with hard-line approaches to tackling hooliganism in the 1980s, which many of her critics felt ignored the idea that trouble at football grounds was symptomatic of wider social problems.
Ted Croker, then secretary of the Football Association, made such a point to the Prime Minister when summed to Downing Street in 1985, telling her: "These people are society's problems and we don't want your hooligans in our sport, Prime Minister."
Her plans to tackle hooliganism included a scheme to introduce compulsory ID cards for fans. The scheme, had it become law, would have made it an imprisonable offence to attempt to attend a match without ID.
It was later dropped when Lord Justice Taylor's report into the 1989 Hillsborough disaster suggested that such a measure would be counter-productive.
Whelan said he was a huge admirer of Baroness Thatcher. "Mrs Thatcher was a very, very special lady and a very special Prime Minister," he said.
"After Winston Churchill, we have probably had two or three really good PMs and she was definitely one of those.
"I only met her once and I just thought she was a fantastic lady. The country could do with another lady, another PM who can do what she did. We shall sadly miss her."
Premier League clubs did not hold one-minute silences when former Prime Ministers James Callaghan and Edward Heath died, both in 2005, although respects were paid after the death of the Queen Mother in 2002. It will be left to individual clubs to decide whether they want to pay tribute.