Phillips, Cooper and Bamford all suffered hamstring injuries during the 2-2 draw at home to Brentford at the beginning of the month and Bielsa has revealed that he expects Phillips and Cooper to be out until March.
The Whites head coach says Bamford is now back healthy but did not initially include the striker in his list of players that he had back available for Sunday's return to Premier League action against Burnley at Elland Road.
Leeds had ten players missing for their home clash against Arsenal which fell one week before Christmas.
Eight of those absentees were due to injuries, Phillips, Bamford and Cooper joined by Rodrigo (heel), Pascal Struijk (foot), Jamie Shackleton (Achilles), Dan James (adductor) and Charlie Cresswell (shoulder) on the sidelines.
Junior Firpo also served a one-game ban for amassing five yellow cards whilst Diego Llorente missed out having tested positive for coronavirus.
Jack Harrison was then withdrawn in the 31st minute of the clash against the Gunners in which Leeds fell to a 4-1 defeat.
A small outbreak of Covid-19 in the Whites squad then led to both Boxing Day's clash at Liverpool and the Tuesday night hosting of Aston Villa being postponed.
The coronavirus cases together with injuries meant United did not have enough recognised first-team players to meet the Premier League requirements.
Providing his latest team news at Friday morning's pre-Burnley press conference, Bielsa said: "For the following game, we recover Junior Firpo, Dan James, Diego Llorente, Robin Koch - who had already returned, and Jack Harrison - who basically didn’t play in the last game as he picked up an injury as soon as the game started - has also recovered."
Asked to what extent the current injuries might impact activity in the January transfer market, Bielsa explained: "We’ve been recovering players.
"Even if Phillips and Cooper will return in March, even if Shackleton and Cresswell will return at the end of January or the start of February, the amount of players that we have is increasing.
"We will see whether, during January, an alternative comes up that we may take advantage of."
Pressed on the latest with Bamford, Bielsa said: "This is the fourth week since Patrick’s injury. Patrick is healthy, but he hasn’t played for four weeks now."
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Thank you Laura Collins