The Brit hopes to return to tennis in time for the grass-court season but will definitely be playing it safe by seeing how he feels before he returns.
The 30-year-old Scot has not played competitively since Wimbledon last year and last week withdrew from this month's Australian Open. I'll be more considered in the tournaments I play, even though I play a conservative schedule anyway in comparison to most of the players on the tour. "I'm going to be competing at the highest level again", he said.
Roger Federer was forced into a six-month injury lay-off during the second half of the 2016 campaign before he enjoyed a renaissance in form to claim two Grand Slam titles previous year but Cowan believes the extended nature of Murray's absence makes his return a tougher task.
He is expected to return home in a week or two to continue his recovery and rehabilitation.
Murray is no stranger to the doctor's knife, having undergone surgery on his lower back at the end of 2013.
He went on to win a second Wimbledon title in 2016 and played arguably the best tennis of his career.
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"He felt that my hip will be feeling better than it did a year ago and, obviously, I was still doing fine a year ago, I was ranked number one in the world. I look forward to returning to competitive tennis during the grasscourt season", he added. I'm aware of that and I'm going to make sure I'm going to do that.
"I've obviously been going through a really hard period with my hip for a long time and have sought counsel from a number of hip specialists". "I've been quoted [many] times for how long it's taken for players to get back from the surgery I've had, and up to 14 weeks is what I've been given".
Murray finished it off by keeping positive and saying he'll keep a light schedule.
"I'm certainly not going to be putting in the same amount of tournaments and effort to try to get to number one in the world".
"I've been fairly competitive with top-50 players in the world practising in Brisbane when I was struggling to move, and I made the quarter-finals at Wimbledon when I literally couldn't walk and was in so much pain", Murray said.
"That is the most encouraging part - that he is desperate to get back into action and if he believes he can do it then I don't think any of us should have a doubt".