The 28-year-old Rogers will play halfback against St George Illawarra at Suncorp Stadium on Saturday night after inking a two-year contract extension until the end of 2026.
Madden, who tore his hamstring in the 14-6 loss to Penrith last week and is also on the books until 2026, may not play first grade again this season.
Jock Madden suffered a hamstring injury against Penrith. (Jason O'BRIEN/AAP PHOTOS)
Teenager Coby Black, also signed for two more seasons, is another half unavailable with a broken thumb
Rogers will have several matches in the No.7 until captain Adam Reynolds returns from a torn biceps injury in round 22 or 23.
If all goes to plan Reynolds will then partner five-eighth Ezra Mam in the run to the finals.
Veteran Reynolds is signed until the end of next year and the Broncos, unless they go to market and sign an elite half, will be looking to Rogers, Madden or Black to make a claim for the halfback jersey post-Reynolds.
Rogers started the season on a development contract but has been upgraded to the NRL top 30 this year along with inking his extension.
Broncos coach Kevin Walters said Rogers "certainly" had the capacity to succeed Reynolds and added that the three-way halves battle would unfold in the future.
"Josh has a great opportunity tomorrow night. He has only had one game for us this year against Parramatta and he was terrific," Walters said.
"I have all confidence in Josh that he can get the job done, particularly with his kicking game. it is very important tomorrow night that we get the right kicks at the right times and Josh will play a big part in that.
"He is a great person and has good characteristics around a No.7 or No.6 so we like what he brings."
Broncos second-rower Brendan Piakura, who injured an ankle in Queensland camp on Thursday, did his own training on Friday and will be given until game day to prove his fitness.
Brendan Piakura faces a late fitness test. (Dave Hunt/AAP PHOTOS)
If he's out 20-year-old prop Va'a Semu will get his debut on the bench.
Walters said he believed Semu could make a strong debut if given the chance as the Broncos aim to end a five-game losing streak.
"We will make the decision tomorrow morning but they are both getting ready to play. I am pretty confident Brendan will be right," Walters said."It is just about seeing how sore (his ankle) is in the morning. He jogged today lightly and it is about Brendan's mindset as well, whether he can play through the pain and get it done, which I am sure he can."Va'a is very capable. He's only had a short career but I would have no hesitation in playing him. We have seen him this year at Souths-Logan and we like what we see."
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