“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 said.
“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.”
Murray, who turns 37 in May, said earlier this year that he wants compete at another Olympic Games before he retires.
The two-time Olympic champion has also indicated he wants to make a final appearance at the French Open, which starts on 26 May.
Murray has only played once at Roland Garros since undergoing career-saving hip resurfacing surgery in 2019, losing to Stan Warwinka in the first round in 2020.
Wimbledon, where he is a two-time champion, begins on 1 July, while the Olympics take place in Paris from 26 July.