Mezzadri claims to have spoken to the world No 4 on numerous occasions about Djokovic.
The pair have been at war during the Indian Wells Masters this week because of the ousting of ATP chairman Chris Kermode.
Djokovic, chairman of the Player Council, led a revolt which will see Kermode step down at the end of the year.
Federer is furious with the decision as he wanted the Brit to remain in power.
But now it has come to light that Federer and Djokovic, who share 35 Grand Slam titles between them, have had bad blood for some time.
“Roger likes emphatic people who value each other,” Mezzadri told Swiss newspaper Blick.
“In this respect he has some difficulty with Djokovic. There were situations in which all had to adapt to his tact.
“They are friendly but reserved with each other.
“Roger told me that although Novak was nice and funny, he did not succeed in classifying him.”
Mezzadri went on to explain that Djokovic’s conduct on court often annoys his fellow Swiss.
One recent incident came at Wimbledon last year when Djokovic was booed by the crowd during his victory over Kyle Edmund.
And his tantrum-like reactions get under the skin of his fellow greats.
“When the crowd supports the opponent, Djoker responds with annoyed gestures,” Mezzadri added.
“Although he is looking for the love of the fans, he always freaks it out.
“For Roger, Novak’s offended reactions reflect the dark side of his character.
“Therefore, the rivalry between them dominates – while with Rafael Nadal in addition to the intensity on the court much respect and sympathy.”