As Labour Party members are balloted on a vote of no confidence in Mr Corbyn today, Ms Cooper fanned the flames of speculation that she may intend to stand again in a potential leadership election.
In a speech this morning at the Centre for European Reform in Central London, she said she was not ruling “anything out”.
“I’m not ruling anything out but I’m also not here standing, launching any campaign or canvassing,” she said, stressing the need for Government to come up with a plan following the vote to leave the EU and subsequent political crisis.
Ms Cooper, who represents Normanton, Pontefract and Castleford, challenged Jeremy Corbyn in the Labour leadership contest in September 2015.
She finished third behind former Health Secretary Andy Burnham.
The result of the secret ballot of MPs is due at around 5pm, and it is expected that a Labour leadership contest will then get underway as votes tip away from Mr Corbyn.
No-one has officially said they will stand against the leader, however more than 40 members of his shadow cabinet and junior shadow ministerial team have abandoned his leadership since Sunday.
Mr Corbyn held a meeting of the shadow cabinet this morning with many vacancies still unfilled, however York Central MP Rachel Maskell was by his side having been promoted to shadow environment secretary.
Ms Cooper said: “Just as the country is divided between city and town over the referendum, a gulf is growing between Labour’s support in the cities and the Midlands and Northern industrial towns that have long been our heartlands.
“Our party is in danger of becoming a party of the cities and university towns.”
“Labour votes in the cities who voted in must not push away the Labour voters in the town who voted out. They are not right wing. “And they are waiting for us to stand up for them.”
She said she found Jeremy to be a “kind and friendly man” on the campaign trail last year but in the European referendum he did not have the “campaigning zeal” the party needed in a tough fight to try and persuade Labour voters to remain in the EU.
She said: “He is losing Labour support across the country – and particularly in the towns and coalfields that built the labour movement in the first place.
“Jeremy would be letting down Labour voters and communities across the country who badly need a strong Labour voice right now, and who badly need a Labour government, if he drags this out any longer. I hope he does the right thing in the party and stands down swiftly because we cannot drift and leave Boris Johnson, Theresa May and Ian Duncan Smith to shape Britain’s future.”