Giving evidence to the Scottish Affairs Committee on Wednesday, the Environment Secretary said that despite speculation he would get a meeting with Mr Trump, no private talks were held between the two men.
He also had a 20-minute conversation with Tory leadership frontrunner Boris Johnson by telephone, and at a joint press conference with Mrs May, said the former Foreign Secretary would do a "great job" as Prime Minister.
Mr Gove attended the state banquet for the US President at Buckingham Palace on Monday, and told Scottish MPs that he "had the opportunity to say a few words" to Mr Trump.
"I think the president may well be placing an order for a dress Gordon tartan. So that’s another example of a successful trading arrangement between the UK and the USA that we’ve brokered.”