Ilias, 18, is out of contract in June and Barca are keen to renew his terms, but there is so far no agreement for him to extend his stay at the Catalan club.
A source has told ESPN, while Barca are open to retaining Ilias, the current financial proposal is a long way short of what the player's camp would accept.
Leeds' interest is being led by sporting director Victor Orta, who knows the Spanish market well, but their pursuit been complicated by the club's poor performances this season.
They are without a manager after firing American coach Jesse Marsch, and any hopes of signing Ilias may depend on Premier League survival, with the club in 19th place, two points from safety.
AC Milan are among a clutch of other clubs to have shown an interest in Ilias. However, the Italian side have not made any promises regarding regular first-team football, while Leeds have.
Ilias joined Barca for a second time in 2017 and came through the academy alongside first-team midfielder Gavi.
The forward has long been rated as one of the brightest prospects at the LaLiga club and made three first-team appearances under Xavi Hernandez last season.
However, amid the backdrop of his contract situation, he has not been afforded any further chances with the senior side this season.
In recent weeks, as Barca suffered injuries and suspensions in attack, Xavi preferred under-19 winger Angel Alarcon to Ilias, who has been in and out of the B team.
Only 13 of his 20 appearances in the Spanish third tier have been as a starter and he has not completed 90 minutes since Jan. 7.
He is serving a four-match ban for getting sent off while a substitute for abusing the referee during Barca Atletic's 1-1 draw with SD Amorebieta this month.