Ms Long-Bailey has long been seen as an heir apparent to Mr Corbyn, with some of his allies backing her as a potential successor.
She stopped short of announcing a formal bid but said if she were to run she would back shadow education secretary Angela Rayner as a deputy.
Ms Rayner had previously been touted as a runner herself, though it was then reported she would more likely go for deputy alongside Ms Long-Bailey’s leadership pitch.
Writing in the Guardian, Ms Long-Bailey bemoaned Labour’s failure at the last election and insisted the party can “win again”.
She wrote: “We can win again, but first our party must 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. 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.”
This comes hours after it emerged Labour party chairman Ian Lavery is considering running , following Mr Corbyn’s announcement after the election that he would stand down in the wake of the party’s landslide defeat.
In a statement, a spokesman for Mr Lavery told the Mirror: “Ian is optimistic about the challenges ahead and knows there is a lot of work to be done to unify the party.
“He has had a tremendous amount seriously considering all of his options at present.”
A new leader is to be in place by the end of March, with the party’s executive body meeting to discuss a timetable for a successor in the new year.
Shadow Brexit secretary Sir Keir Starmer has suggested he could run and is being touted among the favourites by bookmakers.
Two other members of the shadow cabinet, Emily Thornberry and Yvette Cooper, are also set to contest for the position.
Clive Lewis and Lisa Nandy have also positioned themselves as potential successors, while Jess Philips and Dan Jarvis are predicted to announce bids.