Bamford, the £7 million summer signing from Middlesbrough, suffered a knee injury while playing for the Under-23 side last week.
The striker was involved in Friday’s 5-0 win over Bristol City when he picked up this injury. He limped out of the game before half-time.
The report claims that the 25-year-old has undergone a series of scans in the past 72 hours, and the club are yet to confirm the potential length of his absence.
Leeds have sent him for fresh examinations on Monday. It is highly unlikely that he will play against Millwall, but Leeds fans can hope that his injury is not too serious.
Bamford is yet to start a Championship game under Marcelo Bielsa, but he has impressed every time when called upon from the bench.
A serious injury to Bamford would leave Bielsa without an experienced alternative to Kemar Roofe upfront.