The club wants to develop the former Twelve Oaks Golf Club in Highworth into a training ground and offices.
The Robins' chairman, Lee Power said: "Nigel Eady left a significant sum of money in his will to be invested for the benefit of STFC and the community."
Currently the club leases its stadium from Swindon Borough Council.
Nigel Eady was a lifelong supporter of Swindon Town and bequeathed the undisclosed sum from his will.
DBS Consulting is involved in the project and the ongoing talks between the trust and football club.
Managing director, Les Durrant, said: "Discussions have been going on between the Nigel Eady Trust and Swindon Town because the trust want to invest in it, not just for the football club but also for the wider community.
"The discussions have been around the trust taking ownership of the site and the facilities being developed for the football club to be used."
The former golf club was bought by Mr Power a year go but as yet it has no planning permission.
The hope is to create a new gym, treatment rooms, lecture rooms, grass training pitches and a floodlit 4G artificial surface pitch.
On Wednesday evening, the club met the town councillors to talk through the project.
Mr Power added: "We are working closely with the Nigel Eady Trust and the local community.
"We will be developing our proposals in greater detail after further consultation with local people and clubs/organisations over the next few weeks.
"We want this new training centre and pitch facilities to be of benefit to the local clubs as well as Swindon Town."
The aim is to develop the site over the 24 months.
Swindon Town FC hopes to develop new training facilities with the help of money from a trust set up by a former supporter.