Back row forward John Muldoon has suffered a recurrence of a back injury this week and will not take any part in Friday night's pivotal European Challenge Cup Pool 3 encounter.
Other players unavailable for the game due to injury include backs Ofisa Treviranus (leg), John Hearty (hip) and Keith Matthews (calf).
Speaking to the Galway Independent, Bradley said: "Brive beat us when we played them in France and that left us having a lot of ground to make up in the pool. Thankfully, we are now in this position (where matters are in our own hands) but there is still a big battle to face before we can go through.
"Brive are not getting the reward their performances deserve this season but we know they are formidable and probably should have won in Newcastle.
"They have nothing to lose on Friday night and they will come to Galway to have a right crack off us. It should be a great occasion given all that is at stake and we are hopeful that a big crowd in the Sportsground could swing it our way."
Should Connacht triumph, they will set up a quarter-final clash in April away to either Sale Sharks, Worcester or Bath.
CONNACHT (v Brive): Gavin Duffy; Matt Mostyn, Daniel Riordan, Mel Deane, Aidan Wynne; Andy Dunne, Conor O'Loughlin; Brett Wilkinson, Adrian Flavin, Robbie Morris, Michael Swift, Andrew Farley (capt), Michael McCarthy, Johnny O'Connor, Colm Rigney.
Replacements: John Fogarty, Ronan Loughney, David Gannon, Ray Ofisa, Conor McPhillips, Tim Donnelly, Liam Bibo.