Federer, 33, is aiming to win the season-ending showpiece for a sixth time and overhaul Serbian Novak Djokovic to tie Pete Sampras' record of finishing the year as world number one six times.
To do that Federer will first have to progress from a challenging round-robin group in which he has been drawn alongside Murray, Kei Nishikori and Milos Raonic.
The Swiss 17-time grand slam champion, who starts his campaign against Raonic on Sunday, is tipped to meet Djokovic in the final, however, he is not underestimating in-form world number six Murray.
"The margins are so small that I feel we always have to prove ourselves time and again," Federer said. "Definitely Murray wasn't himself the first few months of the year.
"It took him a while to get fully fit again after the [back] surgery [in September 2013]. I was very happy for him to do so well at the end of the year. He put in an unbelievable effort to be here and he has a chance to go higher as a favourite at the tournament.
"Things can change very quickly, so that is why I am always careful with predictions. It is nice to see different faces at the ATP World Tour Finals this year with Raonic, [Marin] Cilic and Nishikori. It will be interesting to see how it will play out. I think the groups are interesting as well."
Murray won three of his past six ATP events to ensure he finished in the top eight in the Race to London after a largely difficult year marred by fitness problems.
And the Scot, who meets Nishikori in his first match, is now setting his sights on a return to the top four with a strong showing at the o2 Arena.
"You know, I'll obviously try to finish in the top four if I can but a few weeks ago it was 'oh is he in the top 10, will he make London' so yeah I'll try to finish in the top four," Murray said.
"I'm not expecting to finish in the top four but if I do it will be a very good effort after the last few weeks."