He tells a story of meeting their father Richard, who recommended that McEnroe start his own perfume range.
"I still don't think the world is a poorer place because it lacks a Johnny Mac perfume," he said, according to extracts published by Mail Online. "Though Eau de McEnroe does have a certain ring to it."
The explosive player mocked Serena Williams for her rage on the court, joking that his "overall body of work eclipses her in this area". He did say, however, that he thinks she is probably the greatest female player of all time.
McEnroe also criticised Sharapova, singling her out for her grunting.
The noise, he said,"takes away from the your appreciation of what they're doing" and should be banned. Men are fine to make noise, he argues, because the pitch is lower.
He does, however, think that women and men should be paid the same.
The book, his third autobiography, is entitled But, Seriously, and lifts the lid on the ongoing rivalry between players.
When Andy Murray appointed Ivan Lendl his coach, McEnroe - whose legendary feud with the Czech player was one of the most memorable in sport - admitted that he was furious.
He described his immediate reaction in the book, writing: "'Ah, no way, he hired Lendl. It's not going to work'. Then I realised: 'Oh my God, it is going to work'. That was even worse."
McEnroe said that he hated Murray's former coach Brad Gilbert so much that when he lost to him in 1986 he stopped playing tennis for six months.
McEnroe described Gilbert as a "world-class talker".
"Murray is always complaining about one thing or another but he doesn't say much the rest of the time so he could have just been driven nuts by Brad's constant chatter," McEnroe notes.
He does, however, praise Lendl for his work with Murray, saying that he got Murray "believing in himself more", improved his fitness and made him mentally tougher.
Most surprising, perhaps, given his work at Wimbledon, is his strident criticism of the tradition of showing respect to the Royal family.
"As for all the bowing and the curtsying - and we're not just talking about the Queen here, we're talking about some pretty minor royals - what was that all about?" he writes.
"This was the class system gone mad, the opposite of a meritocracy where hard work is rewarded and people are respected because they've actually done something, not because they've been born on the right side of the tracks.
"Who were the performers here? The players, right? So why were they bowing to someone else when they were about to provide the entertainment?
"Those people in the royal box should think about bowing to them."
