Central government has provided £19.4 million of emergency funding, leaving a gap of just over £3 million against the projected costs
The position is laid out in a report going before Cabinet next Wednesday (29 July).
In a online statement, the City Council said "These projections only take into account the immediate costs of responding to the pandemic and do not factor in the recovery phase or the impact of any future waves of infection.
"The council is continuing to lobby Whitehall for additional funding, but cabinet councillors will be told next week that unless more money if forthcoming, the authority will be forced to consider in year cuts which could impact on services.
"The costs of tackling coronavirus has significantly distorted the council’s budgetary position. Were it not for the unexpected pressures of the pandemic, the council would be on course to break even against the budget it set last spring.
"However, providing vital support such as an emergency food hub, taking homeless people off the streets and purchasing personal protective equipment has cost many millions of pounds."
At the same time, the council has also seen a drop in income with many services, such as leisure centres and car parks, being closed during lockdown.
Councillor Louise Miles, City of Wolverhampton Council’s cabinet member for resources, said: “Government went on record at the start of the pandemic crisis to say councils would be given the resources to do whatever it takes to look after our vulnerable residents during this unprecedented emergency.
“Since March, the council has been a lifeline to our communities - delivering millions of meals to people shielding at home who have no other source of help. We have taken homeless people off the streets and purchased large quantities of PPE to keep people safe.
“At the same time, lockdown caused our income to drop with less business rates coming in, more people applying for council tax support, leisure centres and car parks closed.
“So far the Government has provided us with £19.4 million in additional financial support, which is very welcome and covers us up to this point. However, we need more money to cover the full costs of this pandemic response if we are to avoid making in-year cuts to local services to pay for this.
“We manage our money well, we plan ahead and make strategic, considered decisions. Were it not for the pandemic, we are on course to break even against the budget we set at the start of the year.
“It is coronavirus which is distorting the position and creating these cost pressures and we do need more resources from Government to avoid Wolverhampton people paying the price for something that is not of their making.”