The 18-year-old centre-back has been a part of the Rangers first-team squad this season and has started two Scottish Premiership games this season.
He is likely to get another starting eleven berth when Rangers take on Dundee in the Scottish League Cup quarter-final at Ibrox on Wednesday night.
Van Bronckhorst has been working on the game of the young defender behind the scenes as he looks to develop him and King stressed that the Rangers boss wants him to improve all aspects of his game as a centre-back.
King also insisted that he is prepared to play in other positions as well in order to help the team.
He said in a press conference: “The boss wants me to improve on everything, I work closely with all of the coaching staff to take on all of the experience I can to improve.
“I’ve not always been a defender, I started out further forward. I’ll play anywhere for Rangers.”
Rangers have received some hammerings in the Champions League this season, which reached its nadir when they lost 7-1 at home to Liverpool last week.
King still wants to play in the competition for Rangers and stressed the importance of sticking together as a team after such big defeats.
“I want to play Champions League games with this football club.
“We have to learn and bounce back from these games.
“It can be tough but we win as a team and lose as a team, we are such a close group.”
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