In reporting on gay chief executives, CNBC and NPR repeated the rumor that Apple CEO Tim Cook is openly gay.

The driver behind both stories was the publication of The Glass Closet: Why Coming Out is Good for Business by John Browne, who resigned as chief executive of British oil giant BP after he was outed in 2007.

NPR talked with Browne – Lord Browne of Madingley – about the CEO landscape. During the interview, he stated: “Certainly, if you look at the S&P 500, there isn't one out, gay CEO.”

A reader wrote in to correct Browne, saying Cook is openly gay, and NPR host Melissa Block read the letter on the air without challenging the assertion.

“Peter Tenney of Baltimore writes: In point of fact, Tim Cook of Apple is openly gay,” Block read.

Similarly, CNBC's Squawk on the Street hosted New York Times columnist James R. Stewart to discuss a profile on Browne he wrote.

“There are gay CEOs in major companies, and I reached out to many of them,” Stewart said on the program. “I got an extremely cool reception. Not one would allow to be named at all.”

“I think Tim Cook is fairly open about the fact he's gay at the head of Apple, isn't he?” co-host Simon Hobbs asked.

“Hmm, no,” Stewart awkwardly replied. “I don't want to comment about anybody who might or might not be. I'm not going to out anybody.” (The video is embedded on this page. Visit our video library for more videos.)

While Cook has not denied the rumor – made persistent by frequent mentions in Out's annual Power 50 list and his strong support for LGBT workplace protections – he's also never publicly discussed his sexual orientation.