"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," Khan told CNN in an interview Monday.
Last week, the White House confirmed that Trump's state visit to the United Kingdom has been delayed until 2018.
The delay comes amid concern that there will be mass protests against Trump in the British capital.
Trump met with UK Prime Minister Theresa May at the G20 summit in Hamburg and told reporters he would be visiting London.
May's offer of a state visit, which typically includes a banquet with the Queen, was made during her visit to Washington in January, just days after Trump's inauguration.
Khan, the first Muslim mayor of a western capital city, 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."
CNN has reached out to the White House for comment.
Khan and Trump's relationship got off to a famously bumpy start over 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, 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.
"At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!'" Trump tweeted.
Khan responded by saying his remarks had been taken out of context because he had been referring to the enhanced police presence.
But 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 UK trip over fears that it would "cause embarrassment to Her Majesty the Queen."