The Robins want to complete a £50million redevelopment of their current stadium, turning it into a 20,000 all-seater ground.
But local councillors are refusing to back the proposals, and are trying to convince the Wiltshire side to move to a new location.
A Robins spokesperson said said: 'At the moment there are two plans - plan A is to redevelop the County Ground and plan B is a move outside of the borough.
'There are clear overtones being made to us to try and woo us to another site, but at the moment our focus is on seeing whether we can redevelop the County Ground site.
'We feel the town needs the football club and the club needs the town. We are Swindon Town Football Club and we want to remain within the Borough.'