The authority is looking for a provider to offer wireless internet at no cost to those who use it - or the council.
The initiative is being led by Sheffield Business Improvement District, or BID, which receives a levy from city centre firms to improve the area in which they operate.
The project relies on a provider offering Wi-Fi at no cost to the council, and paying rent to use ‘street assets’ such as lampposts to provide the signal.
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If approved, the Wi-Fi would cover the Sheffield BID area, which is inside the ring road, along with some public buildings such as the Winter Gardens.
Cabinet member for business and economy and deputy leader Leigh Bramall said the scheme could put Sheffield among the ‘best connected cities in the country’.
He added: “Our ambition is to create the conditions that allow a super-fast, digitally-connected and vibrant city to thrive. Our economy will benefit and Sheffield will become more connected for people using the city centre.
“But we’ll only appoint a provider on our terms – someone who will provide the service at no cost to the public or ourselves.”
A decision on whether or not to go ahead with the Wi-Fi scheme will be made by the cabinet on Wednesday next week. A report to councillors points out the risk that a provider that meets the strict criteria may not come forward.
But Coun Bramall said: “We’ve tested the market and believe that a provider will be able to offer the service we want for Sheffield in exchange for exclusive use of council-owned street assets such as lampposts.”
The council has suggested a number of ways in which Wi-Fi benefits residents and visitors, such as improved access to public services, better contact between public services and the homeless, and reduced isolation.
Several free Wi-Fi schemes, such as on Stagecoach buses or in university buildings, already exist. But their coverage is usually limited.
Should an appropriate bidder come forward, a contract up to 10 years long could be awarded in June. The Wi-Fi service could then launch in December.
Sheffield BID manager Diane Jarvis said: “This is potentially fantastic news for Sheffield and something that we have been working with the council and other partners on for some time - seeing it coming to life for our city centre is very exciting.
“We want to see increased connectivity standards for Sheffield city centre. The implementation of free, public-access Wi-Fi is central to the BID’s plans for encouraging visitors, residents and employees to spend more time here.
“We believe that free Wi-Fi could drive greater footfall, supporting the high street and the local economy, and at the same time make it easier for visitors to access information about the city centre, such as retail and leisure attractions.”
The opposition Liberal Democrat group on the council has welcomed the Wi-Fi plan. In June, Coun Richard Shaw urged the authority to push ahead with a free service.
Speaking this week, Coun Shaw said: “We’re really pleased to see the Labour council have finally got a move on with this project after we suggested it last year.
“If this scheme is successful we hope that they will be ambitious and look to roll out similar schemes in parks and local district shopping centres.”