Aged 34, Arnold Palmer was the last man to do it in 15th edition of the biennial men’s golf competition 62 years ago.
Bradley, 39, finished in a tie for 17th at the BMW Championship last Sunday, to cement 10th place in the USA’s Ryder Cup standings.
Trump added: “Keegan Bradley should definitely be on the American Ryder Cup team – as captain! He is an amazing guy.”
Six of the USA team are known already, with Bryson DeChambeau, Russell Henley, Harris English, Scottie Scheffler, Xander Schauffele and JJ Spaun automatically securing their places.
Bradley will announce his six captain’s picks to complete the 12-man line-up on 27 August.
