Germany lifted a fourth World Cup at the Maracana on July 13, with an extra-time strike from Mario Gotze earning a 1-0 win over Argentina.
Boateng admits that he has struggled to come to terms with the enormity of the achievement but has already set his sights on winning more trophies with his national side and wants Low to be at the helm to help achieve that.
"I certainly hope that [Low] remains as our coach," the 25-year-old said in an interview with Die Welt am Sonntag.
"He has a very large share of the team's success and has developed us enormously.
"It's all happened so fast. I have not even seen our game since then on DVD. All the images, all the emotions - it takes time to process it all. I am going to take that time.
"The European Championships are my next goal. With the Under-21s I have already won it, but not with the senior team. So, don't worry: I'm still far from satisfied."
Boateng delivered an excellent performance in the final against Golden Ball-winner Lionel Messi and the former Manchester City man revealed he has been inundated with praise for what he considers the best game of his career to date.
"I've received about 120 [congratulatory messages]," he continued.
"Many from my friends and former team-mates. This means a lot to me. With the final of the Champions League, it was certainly the best game of my career so far.
"I am not a man who needs self-satisfaction. Of course, I've noticed the criticism, but I had not thought about it after winning the title. I am just looking forward.
"After the game, I called my father, who could not be at the final. He told me that he was very proud. This is much more important than any satisfaction for me."
No official announcement on Low's future has been made, but DFB president Wolfgang Niersbach, revealed on Saturday that he was confident that Boateng would get his wish and the coach would remain in place.
"Everything has been cleared and it is obvious who will be sitting on our bench when we play Argentina, again, on September 3," the 63-year-old was quoted as saying by Kicker.
"We don't need to worry at all about the national team coach."