Murray meets Roger Federer for a 23rd time in the final match of Group B at London’s O2 Arena.
They are currently locked together at 11-11 but Federer has won all three previous meetings here, most recently in the semi-final two years ago.
Federer has arguably been the player of the year despite not winning a grand slam title and has looked impressive so far, beating Milos Raonic and Kei Nishikori in straight sets.
Murray made a poor start to his campaign in losing to Nishikori but bounced back on Tuesday with a straight-sets victory over Raonic.
That kept alive his hopes of reaching the semi-final, with his future in the season-ending tournament also dependent on the outcome of the Raonic and Nishikori this afternoon.
Should the Japanese player win, Murray would have to beat Federer in straight sets to stand a chance. Victory for Raonic, on the other hand, would mean any win for Murray would be enough, while there is also a scenario where he could lose and go through.
“It will be obviously a very difficult match,” said Murray.
“But it will be an exciting match, a good one to be part of.
“We’ve had some very good matches over the years. I hope on Thursday it will be the same.
“It’s nice to have won against him a number of times. It gives me good confidence and belief every time I go on the court against him.
“Hopefully I can get through the group and keep going. If not, playing against Roger is a good way for me to finish the year, as well.
“There’s a lot of positives for me going into the match. It’s nice to still have an opportunity to go through.”
Murray’s rivalry with Federer dates back almost 10 years, with the Scot adding. “These are matches I’ll look back on when I finish playing.
“They’re the matches that I really remember, playing against the top guys in the big events.”