David Topham, the managing director of real estate firm CTP, has revealed that a pair of 'major, household name companies' are set to take up whole floors of 3 St Paul's Place, close to the Peace Gardens on the corner of Charles Street and Norfolk Street.
The developer is 'about to sign a lease' with a national architectural practice on level six of the building, and has 'just instructed lawyers' to move staff from a regional law firm into the fifth floor.
And Mr Topham said other potential tenants had expressed interest in either taking whole floors, or parts of floors.
"We have a list of people who we've got terms out to and that we're negotiating with."
The firm is also pressing ahead with 4 St Paul's Place - the next phase of the office quarter - and expects to announce plans later this year.
Sheffield Council has agreed a deal giving CTP until next March to find more occupiers for the 10-storey building, which offers 78,000 sq ft of Grade A office space. The top two floors are let to engineering consultancy Arup, and Swedish bank Handelsbanken took 3,500 sq ft late last November.
The council hopes to avoid having to buy the building itself. In 2013 the authority agreed to purchase the block one year after completion, unless the company decided to keep the property or sell it on at a higher price.
Mr Topham said: "It gives us greater time to achieve these lettings and then be disposing of the building to the investment market in due course."
3 St Paul's - the final element of the £200m Heart of the City project - was paid for by a 'basket' of lenders, including £6.8m of public money.
Mr Topham said he was confident by next March the building would be ready for sale, 'and the council's covenant, which has secured the building's investment, will not be called on'.
"We've had no cash from the council. The council have assisted in their role as regeneration drivers to help bring forward new investment in the city. If you look at what's happened here, in many ways it's far more far-seeing and proactive."
But he emphasised: "There are other cities that have done similar transactions."
Mr Topham said the office market had been 'subdued' since the Brexit vote, but there had been a significant change since Easter, with occupiers showing more interest and commitment.
Rents were relatively inexpensive at 3 St Paul's Place, he continued - £23 per square foot, per year, around £10 cheaper than other Northern cities.
"It's a very good deal. But they have to move on. Sheffield is lagging behind because it's not got the same critical mass and the same level of offer."
As well as 4 St Paul's, CTP is also looking at putting up two private residential schemes in the city centre.
"In five to 10 years the city is going to be a completely different place," said Mr Topham.
"Compared to many it punches above its weight."