The Whites are expected to make a number of first-team additions this summer after their impressive first season back in the Premier League.
Football Insider claims that Leeds boss Marcelo Bielsa is also considering signing new players ahead of next season.
The report states that the Yorkshire giants are keen to take advantage of Hjelde, who has just 12 months remaining on his contract at Celtic Park.
Despite at the age of 17, the Norwegian made 11 appearances on loan at Ross County last season.
The Scottish giants will likely offer Hjelde a long-term deal in order to fend off interest from the Elland Road outfit.