The "Southern Expansion" bid was announced on Monday with the backing of the Sutherland, St George and South Coast football associations.
Football South Coast is the governing body for the sport in the Wollongong region.
But despite the association supporting the southern Sydney bid, Papakosmas insists it changes nothing for the Wolves, who will push on for inclusion as a stand-alone entity.
Southern Expansion's bid CEO, Chris Gardiner, was bullish in comparing the relative merits of his bid and the Wolves' bid, saying his group's bid would be a "far stronger bid than the Wolves can ever put on".
Papakosmas reacted to Gardiner's comments saying he wouldn't expect anything different from the rival bid.
"It's not a surprise and nothing has changed from our original position," he said.
"There was always talk about a Sutherland, St George and Illawarra hybrid team being put together.
"But is it the best way moving forward for expansion? Is it in the best interests of the Illawarra and South Coast and our juniors in particular? Or is it the Illawarra being thrown a couple of crumbs to jump on board another Sydney bid?
"We're not Sydney we'll never be Sydney. If they're that confident in their bid then that's fantastic, because we're just as confident in our bid."
Papakosmas said the emergence of the new bid, covering an area Football Federation Australia is known to regard as attractive, would not affect what the Wolves were doing.
He ridiculed suggestions the emergence of the new bid would deal them a heavy blow.
"Football South Coast has gone on public record saying they'll support the Wolves and they'll support a hybrid bid. The question is: What's going to be in the best interests of the region?," Papakosmas asked.
"We've already got a home ground, we've already got a fan base and an agreement with Illawarra Stingrays in the premier women's division down here. We've got every single item that is necessary and we're representing a region.
"We're not looking to go outside or include anyone that's not part of what we call home.
"We'll be putting in a very strong, very competitive, very inclusive bid and the reality is that, eventually, we will have a stand-alone presence.
"We will not be selling ourselves short. We have the ammunition that is required and we will not be piggybacking on some sort of merged bid."
Football South Coast chairman Eddy De Gabriele told The World Game in early January that FSC would support a strong Wolves bid if it was obvious that was the best option, but that: "If we get an indication from the FFA that they definitely want to go with the model involving associations joining forces to cover a wider area and won't support a bid from a stand-alone team, then why would we put all our eggs in the stand-alone basket?
"We've got no problem with the Wolves putting together a bid, but we're trying to understand what the best option would be for FSC and support that."
Papakosmas said the Wolves were powering along with their bid to be one of two teams added to the A-League, hopefully in time for the 2018-19 season.
FFA recently announced the release of expansion criteria would be delayed for months, but that the 2018-19 season was still in the frame for possible expansion.
"It's not going to do anyone any good to say 'our bid is better than yours'," Papakosmas said.
"We'll worry about we need to do to get our bid in order and we're more than confident about what's happening down here and the direction in which we're going with new appointees to the board, new sponsors and other initiatives.
"Any talk about what areas FFA is keen on or not keen on is purely speculative. What FFA is keen on is doing what's in the best interests of the game.
"We'll give Illawarra and the South Coast a team that represents Illawarra and the South Coast and you can see in the past some of these hybrid sporting teams that are put together hoping to get that local connection don't work.
"If some sort of manufactured, hybrid team that includes Sutherland, St George and the Illawarra is in the best interests of football in this region, than I'm possibly not the best judge."
