It comes after staff at Sheffield International Venues, also known as Sheffield City Trust, raised concern about the future of their jobs.
The non-profit organisation was formed in 1987 for the World Student Games and looks after 17 facilities across the city including the City Hall, FlyDSA Arena, Ponds Forge, Ice Sheffield and Hillsborough Leisure Centre.
It had to cancel its usual activities and events due to restrictions on social gatherings brought in to prevent the spread of coronavirus.
The council said it is still assessing what financial impact this has had on SIV and it would be reviewing the financial support it gives it.
Before the coronavirus outbreak, it was revealed SIV was ‘haemorrhaging’ cash at an alarming rate and needed to be bailed out by the council with more than £7 million over last year.
In response to concerns about potential job losses, Andrew Snelling, trust chief executive, said: “The past 12 weeks have clearly been unprecedented times for many businesses, not least those of us working in the leisure and entertainment industry.
“We have been in regular dialogue with everyone from across our organisation about the impact this is having on income as events and activities have been cancelled.
“It would be remiss of us to not plan for the future, so we are putting together different scenarios of how our business will operate as and when restrictions are eased.
“As part of this planning we have tried to gauge interest from employees about possible voluntary redundancy.
“To be clear, at this point we are not offering a redundancy option to employees.
“This is not a consultation and, even if an individual expresses an interest, there is no automatic right to voluntary redundancy.
“With so much uncertainty around the ongoing pandemic timescales, from relaxing restrictions to a potential vaccine, as a responsible employer it is only right that we make plans to safeguard as many jobs as possible during this period so we are able to return to business and provide a high level of service to the people of Sheffield.”
At the start of lockdown, Coun Terry Fox, council deputy leader, said: "The closure of SIV facilities will clearly impact on their business. We have been working closely with them on the subsidy the council provides and will review the impact of the current situation with them as it develops."
Coun Mary Lea, cabinet member for culture, parks and leisure at the council, said: "Globally covid-19 has had a huge impact on the leisure industry, and nationally leisure providers have been forced to close their doors during lockdown to prevent the spread of infection.
"We are currently assessing the impact on Sheffield City Trust and our other leisure provider partners in the city.
"Protecting our vulnerable and reducing the spread of coronavirus is our utmost priority, but we recognise the importance of sport, exercise and leisure and the benefits they have on mental and physical wellbeing.
“We’ll continue to work with leisure partners and providers, to rebuild, when the time is right, a safe and strong leisure offer for people in Sheffield."