The Whites welcome Tony Pulis' men to Elland Road in a top of the table Championship clash and could see Cooper return to the starting line-up for the first time since the 2-0 victory over Rotherham United two weeks ago.
The 26-year-old picked up the hamstring issue during the pre-match warm-up at the Liberty Stadium and was subsequently withdrawn from the side ahead of the 2-2 draw with Swansea City.
Cooper miss the trip to Norwich City last Saturday in the league and the defeat to Preston on Tuesday night in the Carabao Cup but Bielsa has now revealed he could well have a part to play against Middlesbrough.
"Cooper has a possibility to play on Friday," revealed Bielsa.
"If he comes back it will be a plus for the team. He is our captain, he is a courageous and important player. If he can't play we have other options with similar qualities."
Bielsa also revealed that midfielder Adam Forshaw will be available following the international break and gave updates on Tom Pearce and Jamie Shackleton who picked up knocks during the League Cup clash at Elland Road with Alex Neil's side.
"For Pearce it's not very important," the Argentine added.
"He just received a kick on his leg which is very painful but it's just a kick. Shackleton it's an ankle problem but we'll see how this evolves. He is a very tough and courageous player. These aspects of his personality will make it easier to come back.
Asked whether both players had been ruled out of Friday's game Bielsa responded: "I don't know. I'm just telling you what I know now."