John McEnroe has proposed a men v women contest to prove his claim that Serena Williams would be ranked "700 in the world" on the men's circuit.
The seven-time Grand Slam champion said Williams was "the best female player ever" but against men it would be an "entirely different story".
Williams, a 23-time Grand Slam champion, responded to McEnroe, asking him to "respect me and my privacy".
McEnroe, 58, said: "I've got a solution. Men and women play together."
"Then we don't have to guess," added the American. "I'm sure the men would be all for it."
Dmitry Tursunov - the male player ranked 701 in the world - also said on Tuesday he believes he could beat American Williams, who is due to give birth in autumn.
"I would hope that I would win against Serena," he told BBC World Service Sport.
The 34-year-old Russian, once ranked as high as 20th in the world, said he did not think McEnroe was "trying to talk women's tennis down" but said "the reality" was that "men are stronger in general".
"Physically I might not be in the best shape of my life but as an overall package I'm much better than my ranking would suggest. She is pregnant, and I'm not.
Williams, 35, who is the most successful female player of the Open era, confirmed her pregnancy in April, just 12 weeks after winning her record 23rd Grand Slam singles title.
"Dear John, I adore and respect you but please please keep me out of your statements that are not factually based," said Williams on Twitter.
"I've never played anyone ranked "there" nor do I have time. Respect me and my privacy as I'm trying to have a baby. Good day sir."
The world number two expects to be back on court as early as January 2018.
History of the 'Battle of the sexes'
Tennis matches between men and women have occurred before, mostly notably back in 1973 when Billie Jean King took on fellow American Bobby Riggs.
Riggs, the world number one in the 1940s, retired in 1951 and at the age of 55 believed he could beat any of the top female players.
King originally declined to play Riggs and Australian Margaret Court - at the time the top female player in the world - stepped in. Riggs won 6-2 6-1.
But later that year, the top-ranked women's player King - 26 years younger than Riggs at 29 - took him on in an exhibition match at the Houston Astrodome and won 6-4 6-3 6-3.
A third 'battle of the sexes' match took place in 1992 between American former world number one Jimmy Connors, aged 40 at the time, and Czech/American Martina Navratilova, who was 35.
The match took place under special rules to make it more competitive - Connors was allowed only one serve per point, and Navratilova was allowed to hit into half the doubles court. Connors won 7-5 6-2.