The Reds, who are currently based at Oakwell, have submitted plans to the council to build a 2,500-capacity stadium and training facility on a site off Broadway which used to be football fields used by Kingstone School.
The development would also include up to eight five-a-side pitches, with the club hoping to finish construction by late next year.
Barnsley Central MP Dan Jarvis said: “Following regular contact with representatives from Barnsley Women’s Football Club, I have been encouraged to hear about the proposals to bring the UK’s first purpose-built women’s football stadium to our town.
“This represents an amazing opportunity for our young women and girls who play, or may want to play football.
“It would lead the way in providing state of the art facilities, while promoting healthy living through participation in sport.
“The facilities would be a fantastic resource for the club, Barnsley and Yorkshire as a whole, and I look forward to working with the club to support their plans.”
The Chronicle revealed last week that two sites on Broadway were being looked at as possible locations for the new 900-pupil Trinity Academy school.
Concerns have been raised that, with Horizon School already nearby, another school would increase the traffic problems in the area.
Barnsley Women’s FC owner Steve Maddock said: “We would be willing to share the site with a school.
“Our training sessions and games would take place in the evenings and on weekdays so would not add much to the traffic.
“We think this is a fantastic opportunity to provide something truly unique and to lead the way in women’s football.”
Coun Tim Cheetham, cabinet spokesman for regeneration and culture, is also supportive of the Reds’ plans.
He said: “The council works closely with all our local sports clubs and, wherever possible, we utilise our resources to facilitate their growth.
“We are extremely encouraged that Barnsley Women’s Football Club have such aspirations and hope that this will help continue the recent momentum brought about by such a successful World Cup.
“Like the council, they are an ambitious organisation and are looking to make Barnsley the focus of investment and success.
“We are very early in the process of considering a range of options, including potential relocation, and are willing to work closely with the club to undertake necessary due diligence so that the club can be self-sufficient and benefit our community for generations to come.”
More on page of this week’s Barnsley Chronicle.