The scheme would see the club share the ground with Bristol Rugby.
The proposal is an alternative to relocation plans for a new stadium at Ashton Vale which is facing a planning inquiry in October.
Ashton Gate would be redeveloped in stages over three years to increase the capacity to over 26,000 seats.
Bristol City FC board member Jon Lansdown said: “Ashton Gate has been the club’s spiritual home for more than 100 years and these plans would improve and enhance the facilities ready for the next 100 years.
“These plans give us a viable alternative to Ashton Vale. The landowners of Ashton Vale remain very confident that they will be successful at the Inquiry in October, but we need to make sure we have an alternative as, regardless of where it is sited, the Club needs a new stadium. We now have a way forward in that regard.”
Sainsbury’s has planning permission to move from their existing site on Winterstoke Road to Ashton Gate, in the event the club moves to a new stadium at Ashton Vale.
A Sainsbury’s spokesperson said: “Whilst we are disappointed that this decision would not provide our customers and colleagues with a new store in Ashton Gate at this time, we do appreciate that the club needs to explore all options available to them to secure their future.
“Whilst we await a decision on the Town & Village Green issue our colleagues at Winterstoke Road will continue to provide fantastic service to our customers.”
City rivals Bristol Rovers are also planning to build a £40m new stadium.
Rover needs to sell their current ground to Sainsbury’s to fund a move to a new stadium at Frenchay on land owed by the University of the West of England.
South Gloucestershire Council has approved plans for a 21,700-seat stadium in Stoke Gifford subject to improvements to local transport infrastructure.
The club must now wait for a final decision from Government on the supermarket plan before getting work underway later this year.
Buckingham Group is understood to be in negotiations with Bristol Rovers about building the next stadium.