Although the Champions League holders only recently hired current boss Santiago Solari on a contract that runs until 2021, there have been reports they are looking for a bigger name to replace him in the summer.
Jose Mourinho, recently sacked by Manchester United in December, has also been linked with a return to the Santiago Bernabeu, while they are also interested in luring Tottenham's Mauricio Pochettino to the Spanish capital.
But ex-West Germany international Schuster, who spent two years at the club as a player and returned for a brief spell as coach, believes World Cup winner Low would be an excellent appointment.
"I spoke with president Florentino Perez at an honorary event and I explicitly mentioned Low," he told Die Welt.
"[Perez] looked at me oddly, as if I had surprised him.
"Germans are very highly regarded at Real. After all, we have done a good job there, I would not be surprised if the Real tried to hire Low next summer."
Solari has been in charge since Julen Lopetegui was sacked in October following a poor start to his debut season as Zinedine Zidane's successor.
He was given the job on a provisional basis at first, but two weeks later the club confirmed he would take the Blancos reins full-time.
However, Real Madrid's goalscoring struggles following last summer's transfer of Cristiano Ronaldo to Juventus have continued and the European champions remain well adrift of Barcelona in La Liga, leading to speculation that Solari could be cut adrift at the end of 2018-19.
Low's future as Germany coach has been in doubt since his side crashed out of the 2018 World Cup group stages and he admitted last month he is open to taking over at Madrid when he returns to club football.
"I am still interested in coaching a club," he said last month. "I think it would be abroad, not in Germany. Real Madrid are an interesting club for any manager."
The 58-year-old's contract with Germany expires in 2022, after the World Cup in Qatar.