The 24-year-old was drafted 19th overall by Tom Coughlin's side in the 2011 draft and has played a peripheral role in his two seasons in New York.
"I think that every corner in this game wants to be the No. 1 corner and so that's just the mindset that I have," Amukamara told the New York Post.
"My goal is just to play in all 16 games this year and I think if I do that, everything will take care of itself."
The Giants begin their pre-season campaign against the Pittsburgh Steelers next week.