Head coach Sean O'Driscoll says goalkeepers with Premier League experience have expressed an interest in a move to Bristol City.
The club are without a keeper after Tom Heaton joined Burnley and Dean Gerken and Lewis Carey were released.
O'Driscoll said: "People are contacting us. The attraction is that we've got a number one position available.
"It's a case of whether they fit in with what we are trying to do at this time from a financial point of view."
Seven players were released by City in the wake of their relegation to League One and the search for a goalkeeper is currently O'Driscoll's main recruitment focus.
The 55-year-old told BBC Radio Bristol: "We have had some really interesting enquiries from some top quality goalkeepers, some with Premier League experience and a lot with Championship experience.
"We are close on one or two things with a goalkeeper, but nothing that really looks like it will get over the line in the next couple of weeks."