A close ally of Mr Corbyn, the shadow business secretary also said she was backing her close friend Angela Rayner as the party's new deputy.
Writing in today's Guardian she did not formally announce her candidacy but said she was considering standing. She also blamed the party's "compromise solution" on Brexit, as well as a lack of trust among voters, for its worst defeat since 1935 at the General Election earlier this month.
And she insisted the party's policy agenda was popular. "We didn't lose because of our commitment to scrap universal credit, invest in public services or abolish tuition fees."
She claimed Labour "can win again" but said the party must first "come together".
"We are strongest when we stand together as a pluralist Labour family. That is why I'm not only considering standing to be leader, but also supporting Angela Rayner as deputy," she wrote.
"Leadership means leading a team, working with every part of our movement and using all our party's talents to fight the Conservatives at every turn and map Labour's route back to power. Millions woke up to a nightmare on December 13. It's our duty to make sure that doesn't happen again."
Ms Long-Bailey is widely viewed to be the favourite among Corbyn supporters, and frequently defended the party's policies on the airwaves during the election campaign.
However, in comments which will be seen as an attempt to differentiate herself from the Labour leader, she wrote: "From ex-miners in Blythe Valley to migrant cleaners in Brixton, from small businesses in Stoke-on-Trent to the self-employed in Salford, we have to unite our communities.
"Britain has a long history of patriotism rooted in working life, built upon unity and pride in the common interests and shared life of everyone.
"To win we must revive this progressive patriotism and solidarity in a form fit for modern Britain."
She also suggested Labour had further to go in giving its members control of the party, writing: "Our promise to democratise society will ring hollow if we can't even democratise our own party."
Despite not having formally declared her candidacy, Ms Long-Bailey is seen as a frontrunner in the contest, with her main rivals expected to include shadow Brexit secretary Sir Keir Starmer and Wigan MP Lisa Nandy. Shadow foreign secretary Emily Thornberry and shadow Treasury minister Clive Lewis are the only two to have officially declared their candidacy.
Labour Party chairman Ian Lavery is also reportedly considering a bid, with a spokesman telling the Daily Mirror he was "seriously considering all of his options at present".
Today Frances O'Grady, General Secretary of the TUC, said that Labour needed to end its factionalism if it was to regain the trust of voters, and said there were "hard lessons to learn" about leadership.
She said it was "not enough to be popular in the party, you have to be popular in the country too".
"I think Jeremy Corbyn was a decent man and he was very popular in the party, but that isn't enough, people are looking for a leader and a programme that is credible, competent and someone who is going to fight for their interests, and Labour wasn't able to achieve that this time," she said.
"If it focuses, sorts itself out, and pulls together like a broad church not just a collection of factional tribes, then it can start looking to win back voters' trust and holding this government to account."
"This Prime Minister is on probation and will be tested early, is he really going to protect workers rights, and protect the NHS against Donald Trump in future trade deals? There are big challenges ahead and we need Her Majesty's Opposition to be fighting fit."