The 17-year-old spent the second half of last season on loan at Ross County, where he was labeled by then-manager John Hughes as the next Virgil Van Dijk.
Leeds have been interested in Hjelde for at least a year, with the club now close to an agreement to bring him to the club.
The news of Hjelde's impending move to Leeds comes from Nettavisen.
His club Celtic are willing to sell the teenager for a reasonable fee, and would link up with Leeds' Under-23 side at first.
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