The Mirror claims West Ham blew the chance to sign Slimani because Brady, a hugely unpopular figure with Hammers fans, annoyed Foxes supremo Vichai Srivaddhanaprabha with comments relating to the dismissal of Claudio Ranieri last year.
The Leicester chief was said to be 'seething' over her comments and ignored the injury-hit Hammers' interest before allowing Slimani to join West Ham's relegation rivals instead.
West Ham reportedly apologised for any offence caused, but Leicester refused to budge in what was one of the big talking points after deadline day and another embarrassing episode for the Hammers' under fire board.
"Well that's ridiculous," Murphy said of Srivaddhanaprabha's stance on The Debate.
"It's ridiculous because if every club didn't deal with another club because of something in the press that they didn't like then nobody would do any business with anybody would they?"
Joining Murphy as a guest on The Debate, former Spurs and Aston Villa boss Tim Sherwood also suggested the Hammers didn't need Slimani anyway as Andy Carroll - although currently injured - is a better player.
West Ham fans have been unhappy for some time with the way co-owners David Sullivan and David Gold are running the club and are equally unhappy with Brady's involvement in the move to the Olympic Stadium and her weekly column in The Sun.