Phillips injured himself during the second half of Sunday's 2-2 draw at home to Brentford and had to be taken off, the midfielder replaced by Mateusz Klich in the 55th minute.
Leeds had earlier lost the services of captain Cooper who also went down injured in the 12th minute and was unable to continue, the skipper replaced by Jack Harrison as part of a tactical reshuffle.
Bamford returned from nearly two months out with an ankle injury as United's third and final substitute in the 68th minute and the striker netted a 95th-minute equaliser but the no 9 suffered a hamstring injury against the Bees.
German international centre-back Robin Koch has been out since August with a pelvic issue but is working his way back although the defender has been ill and will return to training this weekend.
Leeds have also revealed that record signing Rodrigo has been suffering from a heel issue.
Providing an update on their website, a statement from Leeds United read: "Rodrigo has been suffering from bilateral heel pain for some time.
"The player and medical staff have deemed it necessary to reduce his activity for the time being, in order to aid his long-term recovery.
"Robin Koch has overcome his pelvic injury, but has been ill for the last 10 days.
"He will resume normal training again this weekend.
"Patrick Bamford suffered a hamstring injury during last Sunday's Premier League game against Brentford at Elland Road.
"The evolution of the injury is subject to daily assessment.
"Both players have undergone treatment for their injuries and the club's medical staff will structure the next steps in their recovery."
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Thank you Laura Collins