Sky News reported that the pair are among a list of 20 "working peers" 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, the broadcaster said.
A Downing Street spokesman declined to comment on the report, saying only: "We won't be confirming anything in advance."
Ms Brady, who appeared on The Apprentice with Sir Alan Sugar, is a prominent Conservative backer and was reported to have been offered a choice of Tory safe seats to run for Parliament in next year's election.
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.