Apple CEO Tim Cook (photo by Valerie Marchive)

LGBT advocates are urging the new head of Apple, Inc., to make his sexual orientation public amid media reports asserting that he’s gay.

Tim Cook last week became CEO of the $337 billion company — which weeks ago overtook Exxon-Mobile Corp. to become the world’s most valuable business — after former CEO Steve Jobs resigned from his position.

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Justin Nelson, president of the National Gay & Lesbian Chamber of Commerce, said Cook’s act of coming out would help increase what he called the dramatic underrepresentation of openly LGBT people as leaders in the business world.

“What an enormous thing it would be to have an openly LGBT person leading not only a Fortune 500, but a Fortune 50 company,” Nelson said. “There’s severe underrepresentation of LGBT people on boards of directors of Fortune 500 companies, and I think this would send a very serious message that LGBT people should be at that table, they should be in those board rooms.”

If Cook came out as gay, Nelson said the act could encourage senior executives at other businesses to come out as well and allow for the consideration of more openly LGBT people for board positions at Fortune 500 companies.

Nelson said he isn’t in favor of outing closeted LGBT individuals — other than those who actively work against LGBT equality — but noted Cook’s sexual orientation is apparently an “open secret” and predicted that “we probably will hear from him in the not too distant future on this particular issue.”

The main source of information about Cook’s sexual orientation is a report from Gawker in January citing anonymous sources asserting the new CEO identifies as gay.

“After Cook was profiled as a ‘lifelong bachelor’ and ‘intensely private’ elsewhere, we wondered if he might be gay,” Gawker reports. “We’ve since heard from two well-placed sources that this is indeed the case, and it sounds like Cook’s sexual orientation has been the topic of at least some discussion within the company.”

According to Gawker, one source was told Apple executives would support Cook if he publicly stated his sexual orientation — and even would encourage him to make it public as he takes leadership of the company — but added concerns persist about whether Cook’s coming out would affect the perception of the Apple brand.

Apple, Inc., didn’t respond to the Washington Blade’s request for comment on the Gawker report or the sexual orientation of its new CEO.

Denis Dison, spokesperson for the Gay & Victory Fund, said a public declaration from Cook about his sexual orientation would have a positive impact on the larger LGBT community because it would encourage his straight colleagues and others to pay attention to LGBT issues.

“If he is gay and decides to come out and be leading a company that is as prestigious and large and powerful as Apple is, I think that is a net-plus for the LGBT community,” Dison said.

If Cook remained silent about his sexual orientation, Dison said he imagines the new CEO would continue to face pressure to come out as gay because of his public presence.

“There are those in the public eye who are said to be gay or known to be gay who don’t talk about it ever,” Dison said. “Whether or not that’s considered to be in the closet or just folks who don’t want to discuss it publicly, it doesn’t necessarily help the LGBT community or help their fellow LGBT Americans if they won’t talk openly and naturally about their lives.”

Cook has big shoes to fill after taking the reins of Apple from Jobs, who co-founded the company in 1985 at the age of 21. Jobs was later ousted by the board, but returned when the company was close to bankruptcy 12 years later and led the company to become the juggernaut it is today.

The first test for Cook will likely come with the debut of iPhone 5 — an update to Apple’s popular mobile phone — which is set to hit stores in the fall.

Apple, Inc., is known for being an LGBT friendly company — both in terms of its product appeal to the LGBT community as well as its treatment of LGBT workers. In its most recent Corporate Equality Index, the Human Rights Campaign awarded the company a perfect score of 100. Apple has non-discrimination protections for workers based on sexual orientation and gender identity and provides health benefits for LGBT workers in domestic partnerships.