The winger was also left out of Joachim Low's World Cup squad, which came as a surprise to many after a fine Premier League campaign with the champions, but returned to the international reckoning after being called up for this month's fixtures with France and Peru.
Real Madrid midfielder Kroos lauded Sane's ability and potential, but suggested his temperament may need some work.
5 - In the 2017-18 Premier League, Leroy Sane was one of only five players to reach both 10+ goals and 10+ assists, doing so in fewer appearances and minutes played than any other player to achieve the feat. Omission. pic.twitter.com/r3CGGfVqv4— OptaJoe (@OptaJoe) 4 June 2018
"He can be a world-class player, but he needs people who tell him what to do from time to time and to work on himself," said Kroos, who will hope to feature in his country's UEFA Nations League showdown with France on Thursday.
"That's what Pep is doing at the moment with not selecting him. He wants to provoke him a bit.
"It is clear that you have to find a way to bring him to his top performance. If he is at his top performance, he is for us – with his qualities, which are relatively seldom if you are looking at our squad – a player who enriches us.
"He gives us definitely more options for our game, but obviously only if he is able to show that on the field."