Murray had planned to play singles and doubles with his older brother Jamie at Wimbledon.
“My understanding is he is yet to make a decision on whether he is able to play and that there is no clear consensus among the experts he has consulted,” BBC tennis correspondent Russell Fuller told 5 Live.
“The singles start a week tomorrow, so to play singles over five sets would be a miraculous recovery and seem unlikely – but could he perhaps play doubles with Jamie? The doubles start two or three days later.
“Even if he is not fully fit, would he see that as an appropriate way to bring the curtain down on his career?
“Either way it is a horrible situation for him.”
Murray said earlier in June that retiring at Wimbledon or the Olympics would be “fitting”, given his success in both events.
He had previously said he was “not planning to play much beyond the summer” but did not confirm what would be his final tournament.
Murray ruptured ankle ligaments at the Miami Open in March before his ongoing back problem was exacerbated by playing on clay.
He won his first-round match at Queen’s against Australia’s Alexei Popyrin – the world number 48 – in three sets but struggled from the start as he attempted to play through discomfort against Thompson a day later.
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