The trust said it was ‘experiencing considerable pressures this week' due to a combination of factors, including high levels of flu and norovirus, as well as high levels of need.
Chief medical officer at NHS Gloucestershire, Dr Ananthakrishnan Raghuram, said: ‘The two Emergency Departments in Gloucester and Cheltenham are extremely busy, but all health services are dealing with very high levels of need.
‘We are asking the public for their continued support over this period by only accessing the Emergency Departments if it's a life-threatening condition or serious injury and to continue to use services responsibly.'
A report in The Guardian citing internal staff communications said the trust was preparing to cancel operations, urgently discharge 140 patients and restrict admissions.
Elsewhere, Mid Cheshire Hospitals began reintroducing face masks in clinical areas to prevent the spread of flu and other seasonal viruses from 9 January.
Dr Clare Hammell, chief medical officer and deputy chief executive, said: ‘In line with trusts across the country, we're seeing rising cases of flu and other seasonal illnesses which are having a significant impact on our already stretched NHS. It's important that we take steps to address this to protect our patients, visitors and staff.
‘We're asking for everyone's support to stop the spread of flu and other winter viruses. Evidence tells us that wearing a mask can help and without face masks, the risk of transmitting and spreading infections is increased.
‘We will keep these temporary measures under review in the coming weeks. We'd like to thank our patients and visitors for helping to protect themselves, others and our NHS.'