The authority said relocating the station could generate up to 6,500 more jobs and bring in hundreds of millions of pounds in business rates.
The figures emerged after a Freedom of Information request by BBC Look North.
An HS2 spokeswoman said the Meadowhall site provided "significantly better connections to more people and places".
Figures show that the council spent £78,090 on an assessment of the case for a city centre station, £25,525 on "understanding the economic impact relocating the station and £6,000 on a business breakfast with HS2 representatives.
A Sheffield City Council said: "The differences in predicted economic impact between a city centre or an out-of-town parkway location are vast.
"A city centre station will help connect Sheffield to Leeds and Manchester to help create the 'Northern Powerhouse'. An out-of-town parkway station will be a massive economic opportunity lost. "
It was announced in 2013 that a new station linking Sheffield with London and Birmingham via the HS2 high-speed rail network would be situated at Meadowhall shopping centre.
Katherine Button, of HS2 Ltd,  said: "The Sheffield Meadowhall station is the best location to serve the wider South Yorkshire region.
"We have scrutinised other options including a city centre site, but Meadowhall provides significantly better connections to more people and places across the region and at a lower cost, and provides the quickest onward journey times to Leeds, Newcastle and Scotland.
"That is why the majority of Sheffield City Region authorities, as well as Leeds City Region and East Midlands authorities support Meadowhall, and are keen to see faster progress in the coming months.
"The final decision will come from the Government and we anticipate an announcement will be made later this year."
Sheffield City council has spent £190,000 lobbying for a proposed HS2 station to be moved from Meadowhall to the city centre, it has emerged.