The unbeaten 27-year-old American, who fights Sheffield's IBF world welterweight champion Kell Brook at Bramall Lane on Saturday, has stressed that amid ringing endorsements about his potential he is just trying to do as Mayweather has done - stay focused and keep winning.
"I don't let outside things get to me - expectations, I don't let them get to me at all," Spence said.
"So I don't worry about people saying I'm the next Floyd, I'm this and I'm that.
"I just stay level-headed, stay grinding, training, focused, because I know I still have to get to that point when I am the next Floyd Mayweather. That still has to be proven.
"I have to keep winning. That is what Floyd did. He won, beat the best, won belts and made history."
Spence has sparred with and taken advice from Mayweather, who has been one of his most prominent advocates, describing him as a future superstar of the sport who reminds him of himself.
Regarding the five-weight world champion, Spence said: "He just told me to stay focused and not let outside distractions get to me. Stay in the gym, stay working hard, and listen to your coach.
"I look up to him as an athlete, because he stays focused.
"He is a guy that has all the money in the world but he trains like he is broke. He has all the distractions - women, cars, money, everything that could distract an athlete - but he manages to stay focused.
"He has tunnel vision and that is what I respect about him a lot.
"I take it (Mayweather's backing) as a compliment.
"I have to go out there and prove that what he says is true.
"I don't see any pressure at all - I just have to stay focused, keep grinding and have that tunnel vision like he did when he was he was coming up through the ranks."
Spence, who is fighting for a world title for the first time, has no doubt there will be more pressure on his opponent than him on Saturday due to the bout being in Brook's native city.
"There is going to be a lot of pressure on him," Spence said of the 31-year-old.
"I have fought in my home town before and it was a lot of pressure on me.
"It's personal, fighting in front of your fans, family and people you grew up with. There's a lot of pressure on you to perform and there will be more pressure on him than me."
After exiting the London 2012 Olympics with a quarter-final defeat, Spence feels he has the opportunity on Saturday to "right wrongs" by becoming a world champion in England.
He said: "The number one goal when I turned pro was to win a world title, and now, having not got a gold medal, I can definitely go right my wrongs and bring the title back to the US."
