An NHS trust declared a major incident after pressure on beds and services led to long delays for patients being admitted by ambulance.
University Hospitals of Leicester Trust sent out the warning to staff on Wednesday as parts of the emergency department became "permanently full".
The trust runs Glenfield Hospital, Leicester General and Leicester Royal Infirmary.
In an email leaked to the Health Service Journal (HSJ), medical director Andrew Furlong said: "Earlier today we called an internal major incident following five days of increased emergency pressures.
"This has resulted in very high numbers of patients in the emergency department (over 140 at some points); the emergency department resuscitation area being permanently full; and patients being held on the back of ambulances for up to two hours."
The email said that, despite attempting to address the issue over five days, the trust had not seen a significant improvement. The problems were being exacerbated by having "the equivalent of two wards of patients" who did not need to be in hospital.
It added: "Given the current position, we need to make sure that every patient in our beds absolutely needs to be there and consider whether they could be discharged with alternative arrangements in place."
In a second email sent on Thursday, Mr Furlong confirmed the trust was still on an internal major incident but that the situation had not got worse.
He added: "We continue to have a very limited number of inpatient beds for urgent and emergency patients on all three sites."
The trust had taken measures to improve its patient flow, including cancelling planned activity across its children's wards to "free up" clinical staff to help in emergency care, he said.