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The US Open will be staged without fans as scheduled from August 31-September 13 in New York while the postponed French Open will be held from September 27-October 11.
Earlier this month, world number one Novak Djokovic said strict health protocols at the US Open would prevent players from bringing more than one person on their support team to the venue but Murray said that was an arrangement he was fine with.
"Playing the Grand Slams would be my priority," Murray said on Monday. "I think the schedule is tricky and I understand the reason why it is like that.
I don't mind what the situation is, providing it is safe. If I was told I could take one person with me... you can make that work. I'd probably go with a physio and some coaching could be done remotely.
Murray downs Goffin to win virtual Madrid Open title
The ATP and WTA Tours are set to resume in August.
Murray, 33, has not competed since playing in the Davis Cup in November due to complications with his hip but is set to return on Tuesday at a behind-closed-doors tournament in London, the 'Battle of the Brits', organised by his brother Jamie.
"My hip has been feeling better for probably the past three or four weeks. It feels better than it did in March," he added.
Right now, I feel a little bit more confident because I've had more training under my belt, more practice. In March time, I'd only been practising for four or five weeks since I'd had the issues.