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"If you don't think that you can beat the best fighter of all time then what are you in the sport for? I'm trying to be the best ever. So that's what I'm going to try and do. And if I don't do it I've tried it. I think a lot of people are scared to do that," he added.
"A lot of people are scared to say stuff like this and put themselves out there and really have a go at their dream. I'm doing it. I think it should be respected by more people. A lot of people don't even want to try their dream."
But Aspinall admits there's no certainty that Jones will beat Ciryl Gane in their UFC title fight on Saturday.
"I think it can go either way. This is heavyweight MMA at the highest level. The wildest division in the most unpredictable sport in the world. You just never know," Aspinall said.
"I think a lot of people are writing off Ciryl Gane. He's very good. He's very skilful. He's got an unusual style for a heavyweight in the fact that he's really mobile, he's really well balanced, really good on his feet.
"Once Jon Jones gets into a rhythm and he gets comfortable he starts to shut people out completely. He [Gane] has to keep him on the move, he has to be super fit, he has to keep him guessing at all times and not let him be comfortable.
"But we're talking about Jon Jones. We're talking about one of the best fighters ever to grace the Octogon. How's he going to look at heavyweight? We don't know. But I wouldn't be surprised either way, that's for sure."