During an interview with CBS's This Morning, McEnroe was asked if he wanted to apologise to Williams. Solve the problem, and I'm sure the men would be all for this - the men and women play together.
When she saw the results, Williams revealed, "I did a double take and my heart dropped".
Williams, who is engaged to Reddit co-founder Alexis Ohanian, 34, confirmed in April that she was expecting a baby in the autumn.
"People always ask me, 'Can you beat Serena Williams?' " continued McEnroe, who in one of life's happy coincidences just happens to have that new book ("But Seriously") coming out.
Serena promptly clapped back Monday via Twitter, saying: "Dear John, I adore and respect you but please please keep me out of your statements that are not factually based. I've done absolutely nothing for the baby room".
Until then, Serena seems determined to focus on her pregnancy, her honeymoon period with Alexis, and her business ventures. She's pregnant, so maybe I should play her now.
Hear him: "I felt like a door had been opened to a person who made me want to be my best self". And on a given day, Serena could beat some players. "I didn't realise it would create something like this". I've said this 1,000 times.
Pam Shriver, McEnroe's ESPN colleague, said, "I think it's a conversation that we all revisit and have every so often and I think it's fine to have it. And I think that deep down we're talking about something - I can't even believe we're talking about it".
The victor of 23 grand slam single titles posted the photo on her Twitter, along with a message for her fans: "Check out my Vanity Fair Cover".
In an interview, McEnroe was critical of the women's sport and the difficulty of men's tennis in comparison.