The world No 3 had surgery on his back only last week in an attempt to cure a long-standing problem and is said to be recovering well.
The operation had been expected to rule him out for the rest of the season, but he has not yet withdrawn from the season-ending tournament at the O2.
It is understood Murray is very unlikely to play in the eight-man event but he will make a final decision after meeting with medical staff next week.
The Scot’s priority is to be fit for the start of next season, and he does not want anything to compromise his key winter training block in Miami.
Murray is likely to head to America in mid-November, around a week earlier than usual, to begin his gruelling physical preparations for the 2014 season.
It was confirmed yesterday those preparations will include headlining the four-man exhibition Dream Cup in Barbados, which begins on 28 November.
The tournament, which also features Juan Martin del Potro, Nicolas Almagro and Richard Gasquet, has a first prize of a holiday at the luxury Saint Peter’s Bay resort worth $500,000.
Almagro ended the reign of Kei Nishikori as Japan Open champion in the quarter-finals in Tokyo yesterday.
The home favourite, who beat Milos Raonic in the final last year, fought back to level the match after dropping the first set but sixth seed Almagro won the final three games to triumph 7-6 (7/2), 5-7, 6-3.
In the last four the Spaniard will meet top seed Del Potro, who came from behind to see off Alexandr Dolgopolov 4-6, 6-4, 6-2.