The 17-year-old Norwegian has yet to make the first team breakthrough at Parkhead but gained senior experience in the Scottish Premiership last season on loan at Ross County.
The left-sided defender joined the Hoops from Rosenborg two years ago, signing a three-year deal, and Leeds could be prepared to swoop this summer, with the Yorkshire Evening Post reporting that the Premier League giants are keen on the youngster.
Hjelde started seven games and scored one goal during his loan spell at County, playing at centre-back, left-back and left midfield, and earned rave reviews from then Staggies boss John Hughes who tipped him to be the 'next Virgil Van Dijk.'
"Leo is going to be the next Van Dijk - trust me on that," said Hughes, who addressed the Whites' interest in the defender in April.
"The quality he has shown, the physical challenge, playing real men's football and standing up to it - it's been a wonderful experience for Leo.
"Before he came, Leeds United were after him. I think he had to sign an extension to his contract for the loan to go through. He’s got massive things in front of him. He won’t be far away from Celtic’s first-team when he goes back.
“This will do him the world of good. Training and playing with men, getting battered about and coming back for more. He’s got more in the locker. He’s got a great left foot."
Hjelde, who scored for Norway Under-18s in last week's 2-1 friendly defeat by Portugal, is the son of former Rosenberg and Nottingham Forest defender Jon Olav.