Winfrey's longtime partner Stedman Graham piqued interest in the possibility after he told the Los Angeles Times, "It's up to the people. She would absolutely do it."
Gayle King, Winfrey's best friend, continued: "I thought that speech was incredible. I got goosebumps."
"President Winfrey" was the talk of the Hollywood after the media mogul accepted the Cecil B. DeMille Award, the first black woman to do so.
The touchstone of Winfrey's speech was the #MeToo movement. But her message -- "A new day is on the horizon" -- sounded like a campaign rallying cry.
Winfrey told the audience: "For too long, women have not been heard or believed if they dared to speak their truth to the power of those men, but their time is up."
Probably the most extraordinary & inspiring moment I’ve ever witnessed at an award show. I had to dry my eyes before presenting the director’s award right after @Oprah ‘s speech. https://t.co/ItULXMJAkY
And the 63-year-old said: "I want tonight to express gratitude to all the women who have endured years of abuse and assault because they, like my mother, had children to feed and bills to pay and dreams to pursue." Her speech drew a huge response from the audience in the room and those watching at home.
Actress Reese Witherspoon, who presented the talk show host, actress and media mogul with her award, wrote on Twitter: "I will now officially divide time like this: 'Everything that happened before Oprah speech: Everything that will happen after.'"
Congratulations @Oprah! You are an incredible role model. Thank you for your inspiring and moving words and for everything you have done for me personally. You have changed my life. ❤
Comedian Sarah Silverman was one of many tipping the US celebrity to run for president, writing: "Oprah/Michelle 2020."
Actor Josh Gad wrote: "Can we all agree that Oprah deserves a planet named after her."
Meryl Streep was quoted as telling the Washington Post that she wanted Winfrey to run for president.
"She launched a rocket tonight. I want her to run for president," Streep reportedly said after the show ended. "I don't think she had any intention (of declaring). But now she doesn't have a choice."
Actress Evan Rachel Wood wrote: "And now I'm crying. Thank you Oprah for nailing it once again." Singer and actor Leslie Odom Jr commented: "She's running. A new day is on the way." Quincy Jones said it was "an honour" to support Winfrey after she thanked him in her speech.
Oprah Winfrey accepting the Cecil B. DeMille Award at the 75th Annual Golden Globe Awards in Beverly Hills. Photo / AP
Winfrey paid tribute to actor, musician and producer Jones, 84, who was responsible for her landing her role in the film The Colour Purple. She was cast as Sofia Johnson in the Steven Spielberg-directed film, which saw her nominated for a best supporting actress Oscar in 1986.
Jones tweeted: "It's been an absolute honour to support and stand by you since the beginning my dear @Oprah ... From The Color Purple to now. Congratulations and all my love to you ... Well deserved'".
Singer Mariah Carey hailed Winfrey as an "incredible role model". She tweeted: "Congratulations Oprah. You are an incredible role model. Thank you for your inspiring and moving words and for everything you have done for me personally. You have changed my life".
Apollo 13 director Ron Howard described Winfrey's speech as "the most extraordinary and inspiring moment".
Howard tweeted: "Probably the most extraordinary & inspiring moment I've ever witnessed at an award show. I had to dry my eyes before presenting the director's award right after Oprah's speech."
Harry Potter and The OA star Jason Isaacs also enthused about the speech, tweeting: "If you didn't watch Oprah elevating the art of communication and inspiration at the GoldenGlobes, get your children — get your daughters — and do yourselves a favour. Show them how leaders SHOULD speak".
Oprah Winfrey accepting the Cecil B. DeMille Award at the 75th Annual Golden Globe Awards in Beverly Hills. Photo / AP
Stranger Things actress Shannon Purser tweeted: "This is the sermon I needed today. Thank you Oprah."
Maria Shriver, the former wife of Arnold Schwarzenegger, said she was "proud" of Winfrey, adding: "A new day is on the horizon. Yes it is. May we all greet it with hope, resolve and faith. #TIMESUP."
Joan Grande, the mother of singer Ariana Grande whose concert in Manchester last year was the scene of a terror attack, said Winfrey made her proud to be a woman.
She tweeted: "I love Oprah ... she made me so proud to be a woman! Magnificent speech, magnificent career, magnificent woman! #GoldenGlobes."
Singer and producer Brad Walsh wrote: "She is quite literally the Antitrump".
It is not the first time that Winfrey's name has been associated with a White House. She supported both Barack Obama and Hillary Clinton and in the 2016 election drama, Donald Trump had suggested she ought to be his running mate — a suggestion she did not appear to take seriously.
