"When that is, I am not really interested in putting a time limit on it because I am quite happy just now so I do not need to play singles after Wimbledon or at the US Open," he added.
Murray has not competed since he underwent an operation on his right hip in January after the Australian Open, which he had signalled could be his last career tournament.
"I still have quite a lot of work to do before I am at a level where I feel like I will be able to be competitive," he said.
Although the three-time Grand Slam champion and two-time Olympic winner said he had been practicing with Frances Tiafoe of the United States at the Wimbledon facilities, he has not confirmed his appearance at the grass court major, which starts on July 1.
"It is baby steps just now. I am feeling good, pretty much pain free and enjoying kind of just training, practicing, improving all the time," he said.
Murray has been crowned singles champion five times at the Queen's Club, in 2009, 2011, 2013, 2015 and 2016, but never in the doubles.
He has won 45 career titles, including the 2012 US Open, and the 2013 and 2016 editions of Wimbledon.
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