Murray is due to face world number two Roger Federer in a charity exhibition match in Glasgow on Tuesday before he starts his preparations for the Australian Open by playing in Brisbane.
The 31-year-old became the oldest man to secure top spot in the end of season rankings.
Murray has been struggling with the hip injury since a five-set French Open semi-final loss to Switzerland's Stan Wawrinka in June.
Andy Murray, a three-time Grand Slam champion whose first major title came in 2012 on the New York hardcourts, was uncertain about his status for the remainder of the season.
Will Roger Federer's style - the variegated and beautiful all-court approach - live on in the next generation?
Rafael Nadal had slipped to as low as 13th in the ATP rankings midway through 2015.
Roger Federer attributed his renaissance to rediscovering full fitness after knee surgery in 2016 and taking a two-month break from the game earlier this year.
A semi-final run in Montreal would see the Spaniard supplant Britain's Andy Murray atop the rankings.
World No. 1 Andy Murray has a history of standing up for equality in professional tennis.
Sam Querrey sent defending champion Andy Murray crashing out of Wimbledon on Wednesday, reaching his first Grand Slam semi-final at the 42nd attempt.
Third seed Federer reached his 50th Grand Slam quarter-final and 15th at Wimbledon with a 6-4, 6-2, 6-4 win over Grigor Dimitrov.
Defending champion Andy Murray added his voice to the growing list of unhappy players.
Murray needed only 96 minutes to see off the dreadlocked German on Centre Court.
Venus Williams wept at Wimbledon over the "devastation" of a fatal road accident for which she is facing legal action as Andy Murray and Rafael Nadal eased into the second round on Monday.
Andy Murray said knowing he is due to become a father again wouldn't provide extra inspiration as he chases a third Wimbledon title and fourth Grand Slam crown.
Murray will enter the tournament desperately trying to shake off a hip injury which played a part in his Queen's Club title defence coming to an abrupt end in the first round last week.
The 30-year-old Scot and world number one -- who suffered a shock first round defeat at the hands of journeyman Australian Jordan Thompson at last week's Queen's tournament -- will not face any of his fellow members of the 'Big Four' until the semi-finals.
US Open champion Stan Wawrinka, 32, triumphed in a pulsating four hour 34 minute battle of shot-making and endurance and will target a fourth Slam title on Sunday.