According to The Times, the head of chemotherapy for OUH wrote to staff.
A leaked memo, circulated at the Churchill Hospital in Oxford, warned that cancer patients face possible delays to their treatment due to a major shortage of specialist hospital staff.
It also warned that the number of chemotherapy cycles offered to the terminally ill would have to be cut because of a lack of staff trained to deal with medication.
Dr Andrew Weaver wrote "Currently we are down approximately 40 per cent on the establishment of nurses on DTU [day treatment unit] and as a consequence we are having to delay chemotherapy patients' starting times to 4 weeks."
The newspaper said the memo also suggested cutting back on treatment to alleviate symptoms for cancer patients, in some cases from six cycles to four.
He was reported as writing: "I know that many of us will find it difficult to accept these changes but the bottom line is that the current situation with limited numbers of staff is unsustainable."
The claim comes days after the Prime Minister was forced to defend the NHS over concerns about its ability to cope against mounting winter pressures.
In a statement, an Oxford University Hospitals NHS Foundation Trust spokesman cited its record of meeting the national cancer waiting time standard of starting chemotherapy within 31 days of a clinical decision having been made, despite increases in cancer patients.
It added: "We have not made any decisions to delay the start of chemotherapy treatment or to reduce the number of cycles of chemotherapy treatment which patients with cancer receive.
"The internal email from Dr Andrew Weaver sets out some of the challenges facing our chemotherapy service, with his ideas for how to tackle these issues, and invites constructive comments and alternative proposals from other cancer doctors and clinical staff.
"However, it does not represent a change to our formal policy for chemotherapy treatment. No such change has been agreed by Oxford University Hospitals NHS Foundation Trust.
"We would like to reassure our patients that no changes to chemotherapy treatment have been made or will be made before thorough consideration has been given to all possible options.
"Any decision to change the approach to cancer treatment so significantly would require a thorough assessment of the potential impact on the quality and safety of treatment and care provided to cancer patients, options outlined clearly in writing, and a formal proposal presented to the Trust's Executive Directors for their approval before implementation."
Any changes to treatment would also need to comply with national guidance.
On Sunday, Theresa May acknowledged more needed to be done for the NHS before claiming that funding is not the sole issue facing the service.
The Prime Minister added thousands of cancelled operations were "part of the plan" amid concerns over the NHS in England's struggles to cope with mounting winter pressures.
Mrs May also sidestepped questions on long-term funding as she faced Andrew Marr, who said he would not be interviewing her if he had experienced the same delays following his stroke as others have encountered.
In a statement, Rosalind Pearce, Executive Director of Healthwatch Oxfordshire, said: "It is very worrying for patients to learn from a national newspaper that their cancer care and cancer treatment may be delayed. It is time that Oxford University Hospitals NHS Foundation Trust made a full statement and cleared the air about what is going on at the hospital, not just around cancer treatment but all treatment.
"We hear a lot about staff shortages at the hospitals, and the public needs to know what is going on, what the hospital is doing about it, and whether it is going to impact on patients.
"We do not want to told continuously that operations are being cancelled or there is a delay in treatment because of staff shortages or whatever reason. The hospital authorities should be more positive and tell the public how they are overcoming the difficulties so that the public and patients can be reassured."