The 72-year-old, who is awaiting retrial in New York on rape and sexual assault charges stemming from his landmark #MeToo case, is receiving treatment in the city's Rikers Island prison complex, NBC News reported.
Craig Rothfeld, Weinstein's authorised legal healthcare representative in New York, expressed his "profound dismay at the speculation surrounding his medical condition".
In a statement given to the PA news agency, he said: "It is both troubling and unacceptable that such private and confidential health matters have become a subject of public discourse.
"Out of respect for Mr Weinstein's privacy, we will offer no further comment."
Chronic myeloid leukaemia (CML) is a rare type of cancer that affects the bone marrow and white blood cells, and is "usually treatable", according to the NHS website.
It comes as Weinstein recovers from emergency heart surgery which he underwent in September.
The ex-film producer became one of the most prominent focuses of the #MeToo movement in 2017 when women began to go public with accounts of his alleged behaviour.
He is serving a 16-year prison sentence following a rape and sexual misconduct conviction in February 2023 in Los Angeles related to an incident in 2013 where he appeared uninvited in a woman's hotel room during a Los Angeles film festival.
He is now awaiting a retrial in Manhattan after a 2020 conviction for rape was overturned earlier this year in a majority decision from the Court of Appeal in New York.
Weinstein has vehemently denied all allegations made against him.
The producer of hit movies including Pulp Fiction, The English Patient, Good Will Hunting, Gangs Of New York and Shakespeare In Love has had serious health problems and been admitted to hospital multiple times in recent years.
In July, he was treated in hospital after being diagnosed with pneumonia in both lungs and COVID-19.
The other conditions he was to be treated for included diabetes, high blood pressure, spinal stenosis, and fluid on his heart and lungs, according to a statement from Juda Engelmayer given to the Associated Press at the time.
