The Whites have snapped up young players this summer as they aim to make sure they have enough depth in the Under-23s for head coach Marcelo Bielsa to dip into if needed.
They have zeroed in on Celtic defender Hjelde, a player who has been compared to former Bhoys star Virgil van Dijk.
The Premier League side are now poised to complete the signing of Hjelde and will have him through the door before the window closes.
Hjelde is just 17 years old and was tempted to Celtic from Norwegian giants Rosenborg.
The Scottish side sent him for a loan spell at Ross County earlier this year and Hjelde impressed with his performances at the club.
Losing the teenager is a blow for Celtic as he is rated as a promising talent and is a Norway Under-18 international.
Hjelde is likely to be slotted into the Under-23s at Leeds, where he would play in the Premier League 2 under Mark Jackson.
