The US leader was offered a state visit to Britain by Theresa May, seven days after his presidential inauguration, when she became the first foreign leader to visit the White House.
She said she had extended an invitation from the Queen to Trump and his wife, Melania, to make a state visit later in the year and was “delighted that the president has accepted that invitation”.
But Mr Khan, who has clashed with Mr Trump over his decision to bar people from travelling to the US from mainly Muslim countries and the response to the London Bridge terror attack, has questioned whether it takes place.
“State visits are different from a normal visit and at a time when the President of the USA has policies that many in our country disagree with, I am not sure it is appropriate for our government to roll out the red carpet,” he told CNN.
He added: “If someone has views that I think can be changed I am ready to play my role.
“If you somehow think it is not possible to be a Muslim and a proud westerner I am happy to disabuse you of that idea, whether you are a reporter for CNN or Donald Trump.”
After months of doubt about whether it would take place, amid speculation the US president could have made a surprise stopover after last week’s G20 summit, the government has conceded that the official visit will not take place until 2018.
Donald Trump reportedly told Theresa May he will not make a state visit to the UK until he is guaranteed a “better reception”.
The US President asked the Prime Minister to prepare a “warm welcome” before he agrees to set a date, it has been claimed.
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“I haven’t had great coverage out there lately, Theresa,” Mr Trump told Ms May, according to a transcript of the conversation seen by The Sun.
Ms May replied: “Well, you know what the British press are like.”
But Mr Trump added: “I still want to come, but I’m in no rush.
It leaves open the possibility of a low-key visit to London before the end of this year if Trump is in Europe on other business.
After the terror attack on London Bridge last month that left eight people dead, Mr Trump took to Twitter to criticise Mr Khan after he said there was “no reason to be alarmed” by the increased police presence drew an extraordinary rebuke from Trump on Twitter.
“At least 7 dead and 48 wounded in terror attack and Mayor of London says there is ‘no reason to be alarmed!'” Trump tweeted.
Mr Khan responded by saying his remarks had been taken out of context because he had been referring to the enhanced police presence.
But Mr Trump then tweeted: “Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his ‘no reason to be alarmed’ statement. MSM [mainstream media] is working hard to sell it!”
Earlier this year, more than 1.8 million people signed a petition seeking to block Trump’s trip over fears that it would “cause embarrassment to Her Majesty the Queen.”