Khan marked his Las Vegas debut on Saturday night with a convincing win over Devon Alexander at welterweight and wants to take on Mayweather in May.
But the WBC and WBA champion is talking up a super fight with Manny Pacquiao instead and was quoted as saying: “No one knows who Amir Khan is.”
Khan said: “I want the fight, but is Floyd going to take the fight? Is Floyd going to give me that chance? That’s something we’re all waiting to hear from Floyd Mayweather.
“I’ve been asking for the fight for the last two or three years. Now he needs to come back to the press and say, ‘I want the fight with Amir Khan’.
“I know I’m touching distance away from that super fight. I think I’ve proven myself many times and I think this time I’ve proved myself in the biggest way so he has to take the fight. What else do I have to do?
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“I have a bigger name than [Marcos] Maidana did or Victor Ortiz. I’m one of the biggest names in boxing. I know if I can bring Floyd Mayweather to Britain then I’ll sell out Wembley Stadium. How big does he need my name to be?
“I think these are little excuses. I’m sure people realise that. It seems to me he doesn’t want to fight me. I have the speed, dexterity, accuracy, movement, power; I think it’s something that he doesn’t really want to mix with.”
Khan pulled out of a prospective fight against Alexander last year because he thought he had landed Mayweather only for the 37-year-old to chose Maidana as his opponent.
That left the Bolton fighter without a fight for 14 months until he outpointed Luis Collazo in May.
He insists he will not make the same mistake again and wants to fight in May regardless of whether Mayweather agrees to take him on, but the prospect of an all-British contest with IBF champion Kell Brook does not appeal.
“I’m not really interested in the Kell Brook fight,” said Khan. “I’m looking at the biggest names in boxing. Floyd Mayweather, Manny Pacquiao, I think that’s where I belong.
“If the fight doesn’t happen with Floyd then maybe Manny Pacquiao is another option.
“I’d like to fight in May to keep myself busy and sharp. I think that helps me.
“It’s very frustrating. It’s just a waiting game. But this time I’m not going to wait and pull out of a fight. If it’s not Mayweather, then I’m going to have to look at other opponents, but if it is Mayweather then I’m going to grab it with both hands and put on a great performance.
“I really believe I can beat him. The way I fought and the way I’m learning, I’m getting better and stronger. I really believe I have his number and maybe Floyd knows that as well.”
Khan, meanwhile, is to donate the shorts he wore in beating Alexander to raise money for the school in Pakistan where 132 schoolchildren were shot dead by the Taliban on Tuesday.
The shorts have 24 carat gold thread woven through the waistband and cost around £30,000.
Khan, who is of Pakistani heritage, said: “I’m going to be donating them towards what happened in Pakistan. I want to rebuild the school and strengthen the security over there.”
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