"State visits are different from a normal visit and at a time when the President of the US 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," Mr Khan told CNN in an interview on Monday.
Last week, the White House confirmed that Donald Trump's state visit to the UK has been delayed until 2018.
Mr Khan, the first Muslim mayor of London, did not, however, rule out meeting with the US President, if offered the chance.
"If someone has views that I think can be changed I am ready to play my role," he told CNN.
"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."
Mr Khan and President Trump's relationship got off to a famously bumpy start over Mr Khan's opposition to Trump's decision to bar from the US people from a list of mainly Muslim countries.
Then, after a terror attack on London Bridge last month that left eight people dead, Mr Khan's reassurance to Londoners that there was "no reason to be alarmed" by the increased police presence drew an extraordinary rebuke from Trump on Twitter.
Mr Khan responded by saying his remarks had been taken out of context because he had been referring to the enhanced police presence, reports CNN.
Earlier this year, more than 1.8 million people signed a petition seeking to block Trump's UK trip over fears that it would "cause embarrassment to Her Majesty the Queen".