UPDATE, January 6: Pompeo told Senate Majority Leader Mitch McConnell he doesn’t plan to run for Senate, The Washington Post reports. So that appears to quash the chance of Grenell being nominated for secretary of State.

There’s a possibility — a slim one, but a possibility nonetheless — that the successor to homophobic Secretary of State Mike Pompeo could be a gay man.

Ambassador to Germany Richard Grenell, the highest-ranking openly gay official in Donald Trump’s administration, has been mentioned as a candidate for the top post at State should Pompeo decide to run for U.S. Senate from Kansas to replace Pat Roberts, a fellow Republican who’s retiring. Pompeo represented Kansas in the U.S. House before becoming Trump’s CIA director and then secretary of State.

Pompeo is on the record as saying he’s not running for Senate, but he actually has been sending “mixed signals,” The Washington Post reports. Trump has been floating the names of various replacements, including Grenell. The leading contenders, however, are National Security Adviser Robert O’Brien and Treasury Secretary Steven Mnuchin, according to the Post.

If nominated and confirmed, Grenell would be the nation’s first openly LGBTQ Cabinet member. A conservative, he’s not necessarily popular with LGBTQ people — or women or Germans. He denounced gay Democratic presidential hopeful Pete Buttigieg for calling out Vice President Mike Pence’s anti-LGBTQ record; the idea that Pence is homophobic is a “hoax,” Grenell said. He is known for insulting powerful women, such as Hillary Clinton and Rachel Maddow, based on their appearance; he had claimed he was trying to be funny. And he has offended Germans with his criticism of the nation’s foreign and domestic policies, to the extent that some German politicians have said he should be recalled from his ambassadorial position.

“The German government has complained about Grenell’s aggressive style, but that’s actually a selling point for Trump,” the Post notes.

Grenell is in charge of the Trump administration’s effort to decriminalize homosexuality worldwide (even as the administration enacts anti-LGBTQ policies in the U.S.), although the president himself seemed oddly unaware of the project when questioned about it last year. Grenell hosted an event to highlight the initiative at the United Nations last month. In another pro-LGBTQ move, he authorized the flying of the rainbow flag at the U.S. embassy in Germany last summer for Berlin Pride, apparently in defiance of a Trump order not to display the flag on official flagpoles at embassies.