Wigan chairman Dave Whelan and his Reading counterpart Sir John Madejski would welcome a tribute to the late Baroness Thatcher during the weekend fixtures.
Neither the Premier League nor the Football League have asked clubs to hold a minute's silence - or applause - in relation to the former Prime Minister.
The Football Association, who preside over Wigan's FA Cup semi-final against Millwall, is also yet to make such a request.
Whelan believes a symbolic gesture would be fitting, though.
"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."
Madejski favours a silence, but with the Royals facing Liverpool - where Thatcher was a particularly unpopular figure - that seems an unlikely outcome.
"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," he told Radio Five Live.
"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."
Reflecting on the possibility of a silence being spoiled by dissenting factions, Madejski added: "Obviously I can appreciate that perhaps some people won't pay attention to it which is sometimes the way at football but I just think 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."