Plans for the new venue have been put on hold during this season as the club look to secure the land they need.
They still fully intend to have the world’s first purpose-built women’s football stadium and will target sell-out crowds of about 10,000.
Albion generally play at the Broadfield Stadium in Crawley and will be back there for WSL action on Sunday when Liverpool visit.
But the vision is to be in their own place, closer to Brighton.
Barber, Albion’s deputy chairman and chief executive, said: “The plans for the women’s stadium have taken a little bit longer to come to fruition than we would have liked.
“Securing the land we need to put another stadium on is, as we know from the experience at the Amex, not easy in a city like this.
“But we have had wonderful support from Brighton and Hove council, wonderful encouragement.
“We are very, very close now to finalising exactly where we want to put it, what we want it to look like, what size it needs to be.
“But we are more convinced than ever that finding the right-sized stadium for our women’s team will accelerate the growth of the women’s game.”
Barber described Crawley as “wonderful” hosts but is keen to get the team to their own venue and said there are no suitable existing stadia in or close to Brighton and Hove.
He added: “The Amex unfortunately at the moment is too big. Every time we open up the stadium, it costs us a lot of money but that is not really the main problem.
“The main problem is that our women’s team are playing in front of 3,000 or 4,000 or 5,000 or 6,000 people at the Amex which makes it a very empty stadium for them.
“It’s not a great environment to play in, in front of lots of empty seats.
“We want to find a stadium that will be the right size for the audience for our women’s team at this point in their history and our club’s history.
“We want to be able to grow that from the 2,000 or 3,000 people we get at Crawley or the 4,000 or 5,000 we get at the Amex to a regular 10,000 attendance, where the stadium is sold out, there is a great atmosphere, the teams that visit us feel a little bit intimidated coming to a full stadium every week.
“And we can design that stadium specifically for our women’s athletes, for our audience at that stadium and genuinely create some history.”
Barber said details which would be examined would be the playing surface, designs of changing rooms and the type of food and drink on sale to fans.
Albion have been keen throughout the season to give more information about the new stadium but there is currently no timescale.
Speaking on the club's official podcast, Barber added: "We have had a couple of setbacks. We are now back in the driving seat.
"We are getting closer but we are not quite there yet."