The Birmingham Yardley MP threw her hat into the ring shortly after the party's defeat in the 2019 general election, having been a prominent critic of Mr Corbyn.
But, abandoning her bid, Ms Phillips said would not be able to "unite all parts" of the party.
She had been considered the third most popular choice for the job, according to polls, following Sir Keir Starmer and Rebecca Long-Bailey.
However, the outspoken politician has now thrown her weight behind Lisa Nandy, who was recently endorsed by the GMB union.
Ms Phillips is still expected to play a huge role in the party and could be chosen for a cabinet position after a new leader is selected.
Here's all you need to know about Jess Phillips:
Who is Labour MP Jess Phillips?
Born and raised in Birmingham, Ms Phillips is the daughter of teacher Stewart Trainer and Jean, the ex-deputy chief executive of the NHS Confederation and chair of the South Birmingham Mental Health Trust.
She revealed in an interview with the Guardian that both her parents were left-wing Labour members who quit the party in protest over the Iraq War.
The 38-year-old studied for a degree in economics and social history at the University of Leeds and a postgraduate diploma at the University of Birmingham, before starting work for the Women's Aid Federation of England in 2010.
In 2012, Ms Phillips was elected as a Labour councillor for the Longbridge Ward, in south-west Birmingham. Just a year later she was selected from an all-women shortlist to contest Birmingham Yardley, a seat she won in the 2015 general election with 41.6 per cent of the vote.
Ms Phillips, is on the soft left of the party, has been an outspoken critic of Jeremy Corbyn's leadership as well as speaking out against the war in Iraq during Tony Blair's tenure.
A mother of two boys, she is critical of the direction the party has taken under Mr Corbyn, and nominated Yvette Cooper to run for the top job in the 2015 leadership election.
While Ms Phillips has never held a role on the front benches, her outspoken nature and fierce campaigning on a number of issues such as equality and tackling violence against women has brought her into the public consciousness.
Her candidacy offered one of the cleanest breaks from the politics of the Corbyn era. Since the party's disastrous defeat at the 2019 general election she has been campaigning for people to join Labour in a bid to change it.
Her public endorsement of Ms Nandy and her second favourite to win, front-runner Keir Starmer, shows she still aims for the party to depart from Mr Corbyn's reign.
She said: "I truly believe that unless we talk to the country on their terms, not just on ours, that we won’t be able to make the gains we need to win an election – and (to) do what everyone in the Labour movement wants to do, and that is make people’s lives better.
“In order to do that, the Labour Party will need to select a candidate that can unite all parts of our movement – the union movement, the members and elected representatives – I have to be honest that at this time, that person isn’t me.
Despite many seats in Leave-supporting areas falling to the Conservative Party last year, there was only a small swing in her constituency despite the fact she was a Remainer standing in a Leave area.
Ex-Labour MP for Great Grimsby, Melanie Onn, said Ms Phillips would be in a "very good position to be able to reach out to ordinary people" if she were to formally stand for the Labour leadership.
After Ms Phillips announced the news of her withdrawing from the campaign for leadership, fellow MP Ms Nandy tweeted: "I’m sorry to see Jess drop out. She has made waves, shown great friendship and I’ll miss her in this contest.”
Shadow foreign secretary Emily Thornberry tweeted: "I’m very sorry to see @jessphillips drop out of the contest. We need to broaden our debate, not narrow it, and force the two favourites to prove they’re up to the fight by pitting them against some real strength.
“Jess is a sad loss in that effort, but we will keep going.”
MP Wes Streeting wrote: "Honesty is the best policy and Jess has it in abundance.
“Although she can’t build the broad coalition needed to rebuild the Labour Party now, she’s recruited thousands upon thousands of new members, amplified the voices of the voters and will play a big role in Labour’s future.”