Watkins confirmed that Swindon had held discussions with Bristol Rovers about ground-sharing while the Memorial Stadium redevelopment takes place.
Rovers had originally agreed a deal to share Cheltenham's Whaddon Road ground but elected to review their options after the original scheme to rebuild the Memorial Ground was delayed.
The favoured option for Bristol Rugby was previously thought to be moving across the Bristol Channel to share Rodney Parade with the Newport-Gwent Dragons.
"Bristol Rugby did phone me hot on the heels of Bristol Rovers, saying 'if Bristol Rovers don't come, we'd be keen to come'," said Watkins.
"I need to open up that dialogue again, because I haven't heard from Bristol Rovers.
The Swindon chief executive revealed that he had received another approach from another rugby club about ground-sharing for the 2009-2010 season.
"Rugby gets a great deal of television coverage so that'd be great for Swindon," said Watkins. "The other thing that I was told was that in a town like Bath, the revenue increases by 30% in the retailing environment when Bath are at home."
The ground's closeness to rail links makes it an attractive proposition
However, Watkins refused to comment on whether that meant that Bath were the club who had approached them. But he was quick to reassure fans who were worried about the impact rugby would have on the playing surface at the County Ground:
"It is the single biggest issue that we would have. At Reading and Watford they put a certain fibre into the pitch that makes it more robust. If we did it we would have to consider it very seriously."
Watkins also revealed that the new owners of Swindon Town have made savings of three-quarters of a million pounds since taking over, including contributions from player salaries, interest payments and bank charges.
The Wiltshire club are predicted to make a �2.4m loss this season.
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