The 53-year-old coach has refuted suggestions that there is an ongoing feud between himself and the German defender, insisting the 24-year-old is one of the best around
Low has come in for criticism from the 24-year-old for what he perceived as a lack of trust, with the trainer electing to pair Per Mertesacker with Jerome Boateng for recent clashes with Austria and the Faroe Islands.
Speaking to Bild ahead of Friday's clash with the Republic of Ireland, the coach said: "We have no problem with each other.
"It is my right as coach to select who I want, but I see Mats on a very high level. He is an outstanding defender.
"He still has to work with us on some details, but he has class and has developed into one of the best centre-backs around - although he is not currently playing.
"We have grown and professionally we are happy. I accept constructive criticism and it is not true that somebody will not play because he expresses an opinion."
Low's men could seal their ticket to next summer's World Cup finals in Brazil by beating the Irish on Friday.