Bristol is "highly likely" to move into the high alert level of Covid-19 restrictions within the next week, the city's director of public health said.
Christina Gray said Bristol was "very close" to moving into tier two, because its hospitals are under "extreme pressure".
Bristol is currently in tier one with a rate of 367 cases per 100,000 people.
The council added that "a number of indicators" would be considered before introducing stricter measures.
"We're in a very, very critical and precarious position," Ms Gray said.
"I would anticipate that it is highly likely that we will be in tier two, or even possibly higher, very soon."
She added: "We're very close [to moving tiers]. We announced this week our enhanced measures, which was described as 'tier one plus', and the reason for describing it in that way was because we were escalating very quickly in terms of our background rates.
"But more concerning, over the last week, our hospital system has come under extreme pressure."
Ms Gray said this was due to patients being treated for the severe effects of coronavirus and a range of other pressures seen at this time of year.
She added that Bristol's residents needed to prepare themselves "psychologically and mentally" to deal with forthcoming restrictions as we head into winter.
A Bristol City Council spokesperson said "a number of indicators" are being looked at before a decision is made to move tiers.
"These include rates of cases, numbers of outbreaks in places like care homes, hospital admissions, and the impact moving between tiers would have on vulnerable people, workers and businesses," the spokesperson said.
"Our situation remains under close review and our 'tier one plus' approach reflects the seriousness of our situation."