Murray was speaking after his first round victory over Richard Gasquet at the Western & Southern Open in Cincinnati.
He beat the Frenchman in straight sets 6-4, 6-4, to set up a second round clash with rising star Hubert Hurkacz, who beat Daniil Medvedev and Roger Federer en-route to the semi-finals at Wimbledon this summer.
The 24-year-old Pole has drawn comparisons to Murray, and said last month he was honoured “to be compared to such a great player”.
Murray is in Cincinnati on a wildcard and was added to the main draw at the US Open, which gets under way later this month, after Swiss ace Stan Wawrinka withdrew.
Despite no longer being at the height of his powers, the Scot will be among the big names at the tournament in Flushing Meadows with both Roger Federer and Rafa Nadal set to be absent.
Novak Djokovic, meanwhile will be hoping for success in the tournament to secure victory in all four tennis Grand Slams in 2021.
