In an open letter, seen by ITV News, the football club's chair, along with NGO Football for Peace and the ROKiT Foundation, urge Downing Street to grant safe passage to 111 players, aged 14-18, and their relatives.
Following the closure of Kabul International Airport, more than 30 footballers were left stuck in the chaos of the Afghan capital as the Taliban swiftly revoked women's right to play sport.
Pakistan allowed the players and their relatives into the country on temporary 30-day visas after British Pakistani footballer Kashif Siddiqi, co-founder of Football for Peace, wrote to Prime Minister Imran Khan.
Earlier this month, they were swiftly moved out of the country via the Torkham border into Pakistan on humanitarian grounds.
But time is running out for the young players and their loved ones, who have just weeks to find an alternative country to resettle, or face being sent back to live under Taliban rule.
The British Government are now being asked to grant UK asylum to the group before their 30 days run out and give them the "chance to succeed here in Britain".
Leeds United Chairman Andrea Radrizzani, Co-Founder of the ROKiT Foundation Jonathan Kendrick, and Mr Saddiqi together signed a letter to the prime minister for a timely intervention "to bring the girls to the home of football, England" and called for a meeting with Home Secretary Priti Patel.
Mr Radrizzani and Mr Kendrick assured the PM they would "guarantee to meet all costs and facilitate all necessary logistics for hosting these young footballers and their families in Pakistan until they are re-settled".
"We are sure you would agree this would be not only a powerful humanitarian gesture but an indication of the UK’s continuing support for women’s rights in Afghanistan at this critical juncture," they urged.
Mr Radrizzani said he will also give the Afghan youth team the opportunity to join the Leeds United Women’s team and help them with their education and finding employment.
Mr Siddiqi, a football diplomat who spearheaded the campaign, told ITV News: “This has been a long 90 minutes of football diplomacy.
"We are now into extra time and call on the prime minister of the home of football to score the winning goal and take us over the line.
"This collective effort is a showcase how football can move faster than politics. My mother’s struggle and flee from Africa to UK taught me that how important it is for society to come together and support during times of crises.
"Faced with the humanitarian crisis in Afghanistan and the plight of these female footballers, we in partnership with others felt there was no alternative but to get them out of that situation.”
Mr Radrizzani added: “Football is a powerful tool in building communities and bridging divides. Unfortunately we have seen the opposite of this unfold in Afghanistan where the Afghan Girls Development National Youth Football Team has had to flee persecution."
"We stand ready to support in any way we can to give the girls a prosperous and peaceful future," he added.
CEO ROKit Foundation Siu-Anne Marie said: "We are really proud to have worked with providing safe passage and lifesaving support to the Afghan women youth team and their families.
"We are honoured to be a part of this incredible journey. Our Chairman – Jonathan Kendrick’s pledge that started and initiated this mission is ongoing. We are excited to see what the future holds."