UK Prime Minister May was clinging to power after losing her parliamentary majority in last Thursday's election, as an agreement with the minority Democratic Unionist Party (DUP) that would keep the Conservatives in power was still not finalised.
"This is still on. Absolutely," 68-year-old Corbyn told the Sunday Mirror, still not giving up his dream of becoming the next British Prime Minister.
He told the BBC that he will call on MPs from all other parties to back his policies instead of May's.
Corbyn said he did not think May had any credibility and it was "unclear" what kind of programme the Conservatives would be able to put forward.
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He said there was a "possibility" of voting down the Queen's Speech and Labour were going to "push all the way" to achieve that.
Corbyn said his party would put down a "substantial amendment to the Queen's speech" based on the main policies in its general election manifesto, with an emphasis on Brexit, young people, and austerity.
Corbyn said his party was "quite ready and able to put forward a serious programme of government", which he said "obviously has massive support in this country."
The Labour leader also said he thought it was quite possible there could be an election later this year, or early next year, which he thought "might be a good thing."
"We can't go on with a period of great instability" he said, adding that the Labour Party was ready to fight another election campaign.
He also suggested he was ready to build bridges with some of the Labour MPs who have opposed his leadership.
Asked if Yvette Cooper and Chuka Umunna - both of whom had been reported to be planning leadership bids if Labour lost seats in the general election - could come back to the front bench, Corbyn said: "I am the most generous person in the world."
May is seeking a loose "confidence and supply" arrangement with the DUP's 10 MPs that would allow her to press ahead with a minority government, after losing her Commons majority in general election.
The Conservatives could command a thin majority with the support of the DUP if they manage to to do a deal with the Northern Irish party.
Labour gained 30 seats in the general election to take its total to 262 seats, but the Conservatives remain the largest party in Parliament with 318 seats.
This would give the Tories the numbers to pass a Queen's Speech on June 19, which will set out their legislative agenda.
But shadow chancellor John McDonnell said he believes there is a majority in Parliament to maintain the winter fuel allowance and "triple lock" state pension guarantee, two policies the Conservatives proposed changing in their manifesto.
He told ITV: "I believe the DUP is in favour of scrapping the bedroom tax. There's a whole range of issues like that where we think there'll be a majority in Parliament."
"We all need to pull together to take on Theresa May and take on the Tories," she told Sky News.
She did not rule out accepting a job in Corbyn's shadow cabinet, but said she did not want to be "presumptuous".
She said the Conservatives' planned deal with the DUP was "dodgy" and "unsustainable" - and Theresa May's position was "not remotely tenable" because she lacked the skills to hold together a minority government, which has to be more open and collegiate.