Bamford will miss a fourth straight game with the knee problem he suffered before last weekend’s 3-2 win at Aston Villa while club captain Cooper is not ready to return from a bout of knee surgery earlier this month.
Leeds expect Bamford, their £7m striker, to be available in the early weeks of January but Bielsa confirmed that he would not be fit for Tuesday’s clash with Nottingham Forest at the City Ground.
Cooper is back in training less than a month after going under the knife but will see his Championship return delayed until Leeds host Derby County on January 11.
The meeting with Forest completes a glut of four league games in nine days for Leeds.
United have taken six points from three so far but saw a seven-match winning streak ended by a 2-0 defeat to Hull City on Saturday.
Bielsa, who has been forced by injuries to pack his bench with development-squad players, fielded an unchanged line-up against Hull and said he was confident his players were coping with the physical demands of the festive fixture list.
He admitted, through, that the clash with Forest would ask more of his side as they looked to defend a three-point lead at the top of the Championship.
“Until now the team gave a good response, a positive response,” United’s head coach said.
“We ran enough (against Hull) and we dominated the game. When you don’t dominate a game you make less effort.
“Until now the tolerance from the players has been good but the fourth game we’re going to play will be the most demanding one because we’ve already played several.”
Forest were expected to make a strong bid for promotion under head coach Aitor Karanka but the Spaniard is under pressure after a 1-0 defeat at Millwall left the club six points adrift of the top six.