Left-back Anderson, 17, signed a professional contract at Celtic Park in January 2020 after moving from Blantyre Soccer Academy in Glasgow.
He was part of the Celtic Under 18s side, coached by former Leeds loan defender Darren O'Dea, who were furloughed by the club in January.
Anderson has represented Scotland at Under 16 level on three occasions and played in the Victory Shield against Wales and the Republic of Ireland alongside current Leeds Under 18 duo Ben Andreucci and Jeremiah Mullen.
Blantyre Soccer Academy chief Jimmy Whelan has tipped the youngster to follow in Kieran Tierney's footsteps.
“It’s fantastic for us as a club, and it’s great to see Matthew doing so well," he told the Daily Record last year.
“He really is one to watch, he is the real deal, and could be like Kieran Tierney.”
Leeds, who already have former Motherwell prospect and Scotland Under 17 international Stuart McKinstry and Scotland Under 19 winger Liam McCarron in their Under 23s set-up, are plotting a fresh round of recruitment for the academy ahead of the new season.
Versatile centre-half Hjelde, also 17, is one of several youngsters on the domestic scene and abroad who are reportedly on Leeds' radar. The Norwegian under-17 international gained senior first team experience in the Scottish Premiership last season while on loan at Ross County, where he earned rave reviews.