Premier League club chairmen Dave Whelan and Sir John Madejski want football to mark the death of Baroness Thatcher with a one-minute silence.
The former prime minister died in London on Monday, aged 87, after suffering a stroke.
The Premier League and Football League will not be asking clubs to mark Lady Thatcher's death at their upcoming fixtures.
"We owe Mrs Thatcher a minute's silence," Whelan told BBC Sport.
As well as Premier League and Football League games this weekend, the FA Cup semi-finals take place at Wembley, which come under the auspices of the Football Association. Whelan's Wigan meet Millwall on Saturday.
It is understood the Football Association has no plans at present to mark Lady Thatcher's death.
"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 said. "We have to say thank you very much for the services the former PM has given us."
And Reading chairman Madejski told BBC Radio 5 live: "We have got to appreciate that Margaret Thatcher was a world leader who did so much for this country. So much that she deserves a minute's silence.
"The funeral's going to take place at St Paul's 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."
However, Reading later said they were already planning to hold a minute's silence before Saturday's home fixture against Liverpool - to mark the anniversary of the Hillsborough disaster.
A club spokesman said: "With the game falling two days before the 24th anniversary of the tragedy, plans began last week for a fitting tribute to the 96 supporters who lost their lives.
"The Royals contacted Liverpool FC and spoke to the Premier League earlier today and they of course agreed it was absolutely correct to pay respect on such an occasion."
Lady Thatcher was Conservative prime minister from 1979 to 1990 and Whelan admitted he had huge admiration for her.
"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."
One-minute silences were not held in the Premier League when former Prime Ministers James Callaghan and Edward Heath died, although respects were paid after the death of the Queen Mother. It will be left to individual clubs to decide whether they want to pay tribute.
Whelan said he could not understand why large sections of the population, especially in the north of England, did not want to mark her death.
But Madejski, a high-profile donor to the Conservative Party in the past, said: "Obviously I can appreciate that perhaps some people won't pay attention to it [a minute's silence], which is sometimes the way at football, but she was such a colossus in terms of the world stage that she deserves that respect from the whole nation.
"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 speaks volumes and I think that outshines things that might not be considered so brilliant like the poll tax and so on."
Manchester United opted not to have a one-minute's silence prior to Monday's derby defeat by Manchester City and Whelan, who was travelling back from a holiday in Barbados at the time, said he disagreed with that view.
Margaret Thatcher's former sports minister, Richard Tracey, shared that view and told 5 live: "Frankly I think it's rather cheap that they decided not to show any sort of respect for her, because, to be honest, she did really deliver what football is today, particularly with the Taylor report, and the all-seater stadia.
"Football was in a bad way when she was prime minister, and we saw all the changes in her time, and they should pay tribute to that."
The county cricket season starts on Wednesday but so far no team has any plans to mark the former prime minister's passing.
However, the England and Wales Cricket Board is advising counties to fly flags at half-mast on Wednesday, 17 April - the day of the funeral.
An ECB spokesman said: "Given that it will be a 'ceremonial funeral' and having taken advice from government, it is recommended that the appropriate protocol would be for first-class counties to fly flags within their venues at half-mast on the day of the funeral itself, rather than holding a minute's silence."
Meanwhile, Premiership Rugby has said it will leave the 12 clubs to decide if they wish to hold a minute's silence. No clubs have informed it that they will do so.