The 52-year-old coach has been mooted as a possible replacement for Jose Mourinho when the Portuguese trainer decides to leave the Santiago Bernabeu.
Earlier in the week, Spain coach Vicente del Bosque stated that Low is ready to take the reins of the likes of Madrid and Barcelona, and Ozil had nothing but praise for the Mannschaft boss.
"He is a very good coach, one of the best in the world," Ozil told Express. "If he could coach Real Madrid? Of course, why not?
"He has the quality to do it."
Ozil then came out in defence of Madrid and Germany team-mate Sami Khedira, saying: "I do not understand the criticism targeted at him.
"He plays regularly at the best club in the world. You can always count on him, he always plays at 100 per cent.
|4/5||Real Madrid are 4/5 to win La Liga in 2012-13 with William Hill|
"I am proud to be able to play with him for Germany and at Madrid. He has improved a lot. He is one of the best No.6 players in the world."
The 23-year-old attacker has been a key player at Madrid since joining Los Blancos from Werder Bremen in 2010 in a reported €15 million transfer, and he underlined he is not thinking about a new challenge just yet.
"I still have a contract until 2016," Ozil added. "I really like the city of Madrid. The sun is often shining and I have many friends there.
"I do not know what the future holds, but I am happy at the club."