The Wall Street Journal was attacked for using a 1993 image of Miss Kagan, who was nominated for the top court by President Barack Obama this week, holding a bat during her time as a teacher at the University of Chicago.

Critics have claimed the sport is regarded as a "lesbian" pastime in the minds of many Americans and the picture was used to allude to rumours about her sexuality.

John Wright, of gay newspaper Dallas Voice, told Politico: "Personally I think the newspaper, which happens to have the largest circulation of any in the US, might as well have gone with a headline that said, 'Lesbian or switch-hitter?'."

Cathy Renna, a former spokesperson for the Gay and Lesbian Alliance Against Defamation, said: "It clearly is an allusion to her being gay. It's just too easy a punch line."

The newspaper has ridiculed the suggestion as "absurd" and the row has surprised many who were unaware softball had lesbian connotations.

However, the New York Post pointed out that the link was so strong that straight softball players had started Facebook pages such as "Not all softball players are lesbians". It interviewed Pat Griffin, an author, who said "throughout history, softball has been a focal point for lesbian women".

Rumours about Miss Kagan's sexual orientation have sparked debate on the ethics of "outing" public figures and the relevance of a judge's personal life.

The White House responded swiftly to a recent Washington Post blog that claimed Miss Kagan would be the first gay person to sit on the court by issuing a strong denial that she was homosexual.

That in turn prompted questions about whether or not that response was demeaning to gays because it implied being gay was something undesirable.

In an attempt to lay the issue to rest, friends of the former dean of Harvard Law School have publicly said she is not gay

One was Eliot Spitzer, the former governor of New York who resigned after he was caught using an exclusive prostitution service.

"I did not go out with her, but other guys did," said Mr Spitzer, a fellow undergraduate at Princeton. "I don't think it is my place to say more."