The Sky Bet Championship club want to relocate their current training base and Thorp Arch academy near Wetherby to a new purpose-built site just over a mile from their Elland Road stadium.
"A report recommending that Leeds City Council enter into formal discussions with Leeds United regarding the development of a new club training ground in the city is set to be discussed by senior councillors next week," the council said.
"If approved by members of the council's executive board on Wednesday, October 18, the council and club will open talks regarding the former home of Matthew Murray High School in south Leeds, potentially becoming the club's official training facilities for senior and academy players."
Leeds' plans to develop a 'community sports village' on land at Fullerton Park, next to Elland Road, could also be provisionally agreed by the council.
"Used also by the academy for weeknight training, this site would become primarily the hub of Leeds United Foundation's wide-ranging sporting and educational programmes and would support the club's aim to be at the heart of the local community," the council said.
Councillor Richard Lewis, the council's executive member for regeneration, transport and planning, added: "Bringing the Matthew Murray site back into use as a training facility in inner city Holbeck makes sense for the club's business, but also sends a powerful message about the club's inclusivity and awareness of its potential to do good in the local community."
Leeds managing director Angus Kinnear said on his club's website: "We thank Leeds City Council for their consideration, we have an ambitious vision for Elland Road and the surrounding area as a centre for elite development and a thriving community sports hub."