Murray had a six-month spell coaching former rival Novak Djokovic between November 2024 and last May but has since spent time away from tennis.
But he has now returned to work with Draper, who looks the most likely of Britain’s current male tennis players to succeed two-time Wimbledon king Murray as a Grand Slam champion.
Draper announced on Tuesday he had split from coach Jamie Delgado, who himself had worked with Murray when the 38-year-old Scot was a player.
“I am very grateful for everything Jamie Delgado has done for me over these past six months,” said Draper.
“He is a world-class coach and a great man.
“In the interim, I will continue to be supported by the excellent team at the LTA (Lawn Tennis Association), with the addition of Andy Murray, who will be supporting me throughout the grass-court season.”
Draper was in the top four of the world rankings last June.
But the 24-year-old has since slid down the standings, spending nearly eight months sidelined by an arm problem and in April he announced he had been ruled out of the upcoming French Open because of a knee problem.
The left-hander played just four tournaments under Delgado, with his best result a run to the quarter-finals of Indian Wells in March as defending champion, which included victory over Djokovic.
Draper, however, has managed just nine matches across five events since returning in February and retired during his first-round clash with Tomas Etcheverry at the Barcelona Open last month.
While he won his first ATP Tour title in Stuttgart two years ago, Draper has never made it beyond the second round on home soil at Wimbledon.
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