The football club won't confirm nor deny the news but has called a press conference for "a major football operations announcement" Wednesday afternoon.
The Bombers are staying tight-lipped but social media spilled the beans early Wednesday morning with many football insiders reporting the rumours.
Brown tweeted "O'Shea is a coach to be excited about" and that "O'Shea has all the qualities you want in a head coach. Well respected, authoritative, ballsy, and a true leader."
When contacted by CBC News, Brown said the hiring was not a rumour to him. It was a done deal.
A three-time Grey Cup champion as a player with the Toronto Argonauts (1996, 1997, 2004), O'Shea played 16 seasons as a linebacker in the CFL for the Argos and Hamilton Tiger-Cats from 1993 to 2008.
The 43-year-old O'Shea has been the special teams coordinator for the Argos since 2010.
The Bombers have invited media and fans to the downtown Fairmont Hotel at 2 Lombard Place for their announcement, which will take place in the Wellington ballroom on the main floor at 12:30 p.m.
Doors will open at 11:45 a.m.
The team has recently made a number of operations announcements, including naming Kyle Walters as the general manager, Wade Miller as president and CEO, and bringing on Danny McManus and Ted Goveia as assistant general managers.
The team cleaned out much of its head office this year, dumping GM Joe Mack and head coach Tim Burke, and accepting the resignation of CEO Garth Buchko.