"When he won I wished him well, now I don't care about him," he said.
"I mean it doesn't make any difference to me about him, let's see how well he does. Let's see if he's a good mayor."
A spokesman for Khan told the Huffington Post the views of Mr Trump are "ignorant, divisive and dangerous - it's the politics of fear at its worst and will be rejected at the ballot box just as it was in London.
"Sadiq has spent his whole life fighting extremism, but Trump's remarks make that fight much harder for us all - it plays straight into the extremists hands and makes both our countries less safe."
The reality tycoon was also pressed on his relationship with British Prime Minister David Cameron who recently criticised him over the same Muslim ban comments, saying they were "divisive, stupid and wrong".
Cameron has refused to retract the comments despite calls from Trump aides to do so. When asked about the relationship between the two, Trump said: "It looks like we are not going to have a very good relationship. Who knows, I hope to have a good relationship with him but he's not willing to address the problem either."
He also denied being divisive and said he was a "unifier" while saying the pending EU referendum for Britain was something for people to make up their own mind about.