Rangnick took charge of United on interim basis in November following the sacking of former manager Ole Gunnar Solskjaer.
But he was unable to improve the club's fortunes, with United eventually finishing sixth in the Premier League under the German.
Rangnick was expected to move into a consultancy role at the end of the campaign but instead left the club permanently following the appointment of Erik ten Hag as manager.
Rangnick is now in charge of the Austrian national side and has advised striker Kalajdzic, 25, to remain with his club side Stuttgart, despite the reported interest from United.
"If he stays in Stuttgart this season, it will not be detrimental to his development."
Manchester United are among a group of clubs that have been linked with a move for Kalajdzic, with manager Ten Hag desperate to bolster his attacking options.
Bayern Munich and Borussia Dortmund were also reportedly interested in the Austrian but have since turned their attention to other targets.
Kalajdzic, who scored six goals in 15 Bundesliga games last season, admits he is unsure where his future lies.
"I don't know myself how my future will turn out but that will become apparent in the next few weeks or as soon as possible, but I can't influence many things either," he told DAZN.
In total, Kalajdzic has scored 24 goals in 58 games for Stuttgart since joining from Admira Wacker in 2019.
A full Austria international, he has scored four goals in 15 appearances for the national side.
Featured Image Credit: Alamy