The Times has reported NHS England is backing the plans, which could mean people with less serious illnesses having to wait longer.
Meanwhile, new targets may be brought in for conditions such as heart attacks and strokes.
NHS England said no final decision has been made, and that any changes would be tested before being implemented from October.
The government has previously said it plans to ditch the target of patients being seen within four hours. Doctors have warned this would have a “near-catastrophic impact” on patient safety.
Emergency units have not hit the target since July 2015.
Prof Stephen Powis, NHS national medical director, said: “The clinically-led review of standards was announced by the Prime Minister in June 2018, and since then I have been working with the Academy of Medical Royal Colleges, Healthwatch England and many others on what matters most to patients, on the clinical issues with the current target regime, and what NHS staff believe will help them provide the best quality care for patients.
“Any recommended changes will be carefully field tested across the NHS, before they are implemented.”
A Department of Health and Social Care spokeswoman said: “As part of the ongoing Clinical Standards Review, the NHS is reviewing performance standards to ensure patients with the most serious illness and injury receive the best possible care in the shortest possible timeframe.
“The NHS is working closely with clinical experts and patient groups nationally and will set out proposals in due course.”