The pair are among a list of 20 “working peers” reported to be nominated by the political parties to be named next week.
Also on the list was major Conservative donor and former party co-treasurer Michael Farmer.
A Downing Street spokesman declined to comment on the reports, saying only: “We won’t be confirming anything in advance. Any appointments would be made in the usual way and are subject to independent vetting and scrutiny by the House of Lords Appointment Commission.”
Ms Brady is a prominent Conservative backer, introducing Chancellor George Osborne onto stage at the party’s annual conference last year, and was reported to have been offered a choice of Tory safe seats to run for Parliament in next year’s election.
A director of Sport Newspapers aged just 20, she later became managing director of Birmingham City before being appointed vice-chairwoman at West Ham in 2010. She appeared alongside Labour peer Lord Sugar in BBC1’s The Apprentice.
Sir Stuart, who left M&S in 2010 and is currently chair of grocery delivery firm Ocado, was appointed by Health Secretary Jeremy Hunt earlier this year as an adviser on recruiting top leaders to the NHS.
More controversial would be a peerage for Mr Farmer, a City financier who has donated more than £2.3 million to the Tories since 2002 and was appointed the party’s co-treasurer by Mr Cameron in 2012.
Reports of new political peers sparked protest from Ukip, whose MEP Patrick O’Flynn said: “Yet more LibLabCon establishment cronies being put into the unreformed House of Lords, I hear. Still a block on Ukip peers.”