Last week, Rovers syndicate chairman Ian Rowden said that the new club was set to take the 'rest' of Sydney and sign more members whilst the Sky Blues will only have the east and maintain the membership number they already have.
But Lugt believes that goal is a long way from being attainable, especially as Sydney FC will have at least six years experience on their crosstown rivals.
"It was interesting to read the comments last week of the chairman of the west Sydney club, [Ian Rowden] that we could have the east [of the city] and they would have the rest," Lugt said.
"I think that's pretty optimistic. Our membership is evenly spread across the city, and I don't believe so much in this geographical divide, as [Rowden] tried to create.
"We go for all the regions, the fans are out there and we believe we have the product - a style and philosophy - that will appeal to fans across the city.
"It's all very well for the west Sydney club to talk about the future - but it's one-and-a-half years before they enter the market and already they are claiming they will have more members than us.
"We certainly accept that challenge and we're pretty confident we will stay ahead of them."
Lugt added that the club was focused on the local community and planned to push Sydney FC more and more until memberships and crowd numbers are at a desirable level.
"In the past, Sydney FC probably didn't make known enough what was already being undertaken," he added. "We are the only club in the league with two fulltime community officers on the payroll, out there all the time.
"We believe those figures [a 10,000 membership] are realistic - whether next season or the year after. In the first season Sydney had an average of 17,000. I'm not going to settle for anything less than that."