The Scot rolled his ankle in the deciding set of his loss to Czech Tomas Machac in southern Florida and withdrew from this month's Monte Carlo Masters and Munich Open.
"Latest update from Andy is that he is now out of the walking boot and will not be having surgery on his ankle," a spokesperson for Murray was quoted as saying.
"His rehab is going well and he is hoping to start hitting again on court soon. As yet he doesn't have a date yet for returning to competition."
Former world number one and three-time Grand Slam champion Murray, who had hip resurfacing surgery in 2019, previously said he did not plan to "play much past this summer" but hoped to compete at another Olympics.
Murray had also said he hoped to play at the French Open, which starts at Roland Garros on May 26.
Wimbledon, where Murray has twice been champion, begins on July 1 and the Paris Games get under way later that month.
