Federer and Nadal have dominated tennis for well over a decade and have amassed 37 Grand Slam titles between them.
However, both stars are reaching the latter end of their careers and the younger generation are soon expected to take over the reigns.
Nishikori, the No 1 Asian player, has become a sporting icon in his native Japan, especially after reaching a career-high ranking of fourth in the world in 2015.
But the 28-year-old has higher hopes than just becoming the best player in his continent as he is now targeting the spot which has been occupied by Federer and Nadal.
“Most of the time I live in the States and I see those guys all the time,” Nishikori said.
“When I was little I used to hit with top players like Tommy Haas.
“I’ve seen them always very close, so I’m really honoured to be the number one Japanese player, but my goal is to be number one in the world, so I don’t feel any pressure from [being the] number one player in Asia.”
Nishikori has slipped down the rankings and now sits at No 20.
But he is hoping to challenge for the Citi Open title this week in Washington to break back into the top 10.
“Well I try to keep motivating myself,” he added.
“Most of my coaches try to pump me up. After coming back from injury, I think I enjoyed this challenge a little more.
“Sometimes I was ranked 30 and I have to come from not being seeded, so I am really enjoying the challenge this year.
“I know it’s going to be tough, but I feel like I’m back again and my wrist is okay and my tennis is back, so I will try to remain [in the] top 10 now, so that is my goal and my motivation.”
Nishikori lost to eventual Wimbledon winner Novak Djokovic in the quarter-finals at the All England Club last month.
But after taking time off, he is now ready to get back into action.
“I’ve been feeling great. I had a couple days off after Wimbledon and started working for almost two weeks,” he said.
“I’m feeling good again. I’ve tried to have a couple good matches. I think it is important to have a couple good matches to gain confidence.
“I might have a tough first round. It is going to be tough. I’m going to try to play focused from the first match.”