While Federer and great rival Rafael Nadal have always had a remarkably genial relationship considering their on-court battles, the Swiss and Murray are regarded as much less friendly.
The British number one is a huge admirer of Nadal and has publicly backed him in the debate over who is the best player of all time, while Federer has on occasion appeared to belittle Murray.
The most recent incident came before the Barclays ATP World Tour Finals in London in November, when Federer questioned the significance of Murray's run of three straight tournament victories in Asia.
Annacone, though, poured cold water on the rumours, telling www.thetennisspace.com: "Roger has the utmost respect for Andy and really understands the complex environment Andy lives in with the media.
"I have read some things that have been written, but as my old protege Pete Sampras said, 'believe nothing of what you read and only half of what you see'.
"It makes for much better reading, and some would say even a better competitive environment, if there is animosity and angst between players, but really my feeling is that they get along fine."
Annacone, meanwhile, became the latest figure within the game to back Murray to break his grand slam duck and argued the subtleties of the Scot's game may explain why he has not done so thus far.
The American, a former coach of Tim Henman and head coach at the Lawn Tennis Association, added: "He is a tremendously gifted athlete and has a very complex game, mental and physical.
"He continues to mature and get better, so I will be surprised if he does not win a grand slam title."