"Now we just need a WOMAN president. I hope you're listening Hillary Rodham Clinton!!! #Hillary2016," one of the many posts read.
#Hillary2016 was trending across the Twitterverse early Wednesday soon after Republican presidential candidate Mitt Romney delivered his concession speech, The Hill reported Wednesday.
Clinton, the current secretary of state, has been regularly asked whether she'd consider another run at the White House and she has always said she wants to leave politics. The former first lady and ex-U.S. senator from New York also doesn't plan to stay on as secretary of state during President Obama's second term.
"I have been on this high wire of national and international politics and leadership for 20 years," she told Marie Claire last month. "It has been an absolutely extraordinary personal honor and experience. But I really want to just have my own time back. I want to just be my own person. I'm looking forward to that."
Clinton unsuccessfully ran against Obama for the 2008 Democratic presidential nomination.
One of the most re-tweeted posts came from Hollywood blogger Perez Hilton:
"Before a winner is declared, I just need to say... #Hillary2016!!!!!!!!!!!!!!!!"
A tally indicated his post was retweeted at least 3,135 times.