The Grade II listed buildings in the Grangetown area of Cardiff were put on the market 18 months ago.
The council has confirmed its received offers for the Victorian buildings, and is looking for a "viable and sustainable solution" for the site.
Local politicians say arts and culture must play a part in any new development.
A deadline for interest parties has now ended and the council has confirmed bids have been received.
A spokesman said the council was now looking to "see the building fully refurbished in line with its listed status, including potential community uses".
It is understood one of the bids involves a mix of business and living space.
The building at Pendyris Street, which is on the edge of Grangetown, is across the river from a new enterprise zone which is seen as key to the city centre's regeneration.
Conditions of the sale for business use have been to include a community room, with hopes also of potentially developing arts and dance studios, an auditorium or cinema, alongside small businesses and work units.
The building was formerly earmarked as a contemporary art gallery as part of the city's failed European City of Culture bid more than a decade ago.
Over the last year, pop-up photographic exhibitions have been held as part of a city-wide festival, as well as a dance and animation event to showcase the building's potential.
The depot was used to house trams, which ran in the area from the early 1880s, and then trolley buses until they stopped running 60 years ago.
The building had been used for repairing council vehicles over recent years but its redbrick facade with arches is listed.
David Drake, director of Ffotogallery - which is looking for a new Cardiff home - has met with universities, arts organisations and innovations group Nesta, about a partnership to develop the building.
He said it was good news a credible developer had come forward and he was keen to speak to them once negotiations with the council were complete.
"We think it's a fantastic space and we'd love to do something again there with the Diffusion festival next year," he said.
"With the BBC's plans for the front of the station, that whole area will be changing in character and it would bring the Tramsheds back towards what's going on in the city centre.
"It's also a very interesting building with a lively residential community in Grangetown and Riverside nearby and it would be fantastic to develop community and cultural provision for that area."
Local councillor Ashley Govier said he was encouraged there had been interest.
"I still want to see a cultural centre, similar to what you see at Chapter but reflecting the different cultures in this area."
Historic tram and trolley bus sheds could become a new cultural centre for the Welsh capital.