The Arsenal midfielder says that claiming the trophy would be a fitting tribute to a coach who has revolutionised the national team since taking over from Jurgen Klinsmann
The Nationalelf have arrived in Brazil seeking their fourth world title and were handed a tough Group G draw against Portugal, Ghana and USA.
The former Real Madrid man says that he and his team-mates want to claim the crown as a thank-you to Low, whom Ozil believes has revolutionised the national team during his spell in charge.
"He's introduced a totally new German national team - one that is really respected all over the world," the Arsenal star told the club's official website.
"Wherever we go, I think opponents are reluctant to play us because we are very strong. If you look at the German team over the last couple of years, you can see that we have continuously played excellent football."
Low, 54, took charge of the side following World Cup 2006 and finished runners-up at Euro 2008 before making it to the semi-finals of both World Cup 2010 and Euro 2012, with Ozil is keen to go a step further in Brazil.
"[Low] is one of the best in the world and we're happy to have him around the team," he enthused.
"I hope he will finally be rewarded because in the past we've lost in the semi-finals or final and to lose when you are so close is always sad."