Tom Watson told a meeting of MPs the move was a 'last throw of the dice'.
Labour deputy leader Tom Watson will hold emergency talks with trade union leaders on Tuesday after a tense party meeting in the House of Commons.
Mr Watson told the Parliamentary Labour Party he had informed Jeremy Corbyn during a one-to-one meeting that he could not carry on as party leader without the support of the party's MPs.
Sky's Chief Political Correspondent Jon Craig said the deputy leader told Labour MPs the trade union meeting was "the last throw of the dice" after they overwhelmingly backed a vote of no confidence in Mr Corbyn last week.
He said: "Tom Watson, the deputy leader, who many Labour MPs look to save the party and rid them of Jeremy Corbyn ... told Mr Corbyn the Labour leader needs to have the authority of the Parliamentary Labour Party, it's not enough just to have the authority of the members. He said also 'the window is closing very rapidly'. However, Mr Corbyn said he was not going to budge, he made it clear he was not going to stand down."
Union leaders are thought to have "reached out" to Mr Watson to try and obtain a negotiated settlement.
Mr Watson earlier met former shadow business secretary Angela Eagle and ex-shadow work and pensions secretary Owen Smith - who are both considering a challenge if Mr Corbyn continues to resist calls to go.
Both were said to have agreed to hold back while there is still a chance of a negotiated settlement which sees Mr Corbyn step down.
It comes after Mr Corbyn released a Facebook video with a message for rebel MPs that it's his responsibility to "carry on" as leader.
In it, Mr Corbyn makes an appeal directly to Labour members and says he wants to reach out to "trade union affiliates and MPs" repeatedly telling them to "come together" to take on the Tories and campaign for jobs, schools and hospitals.
And he warns Labour rebels that he was elected just nine months ago with the support of 60% of Labour members - making it clear he is going nowhere.
He says: "I have a huge responsibility, I'm carrying out that responsibility and I'm carrying on with that responsibility."
Mr Corbyn lists the successes he has had since taking on the role, including forcing rethinks on tax credit cuts, police cuts, personal independence payments and forced academisation of schools.
And to underline his membership support, he says that in the last week 60,000 new members had joined the Labour party making it the biggest membership in his lifetime."
According to polls most of those members support Mr Corbyn.
On Monday morning Ms Eagle told Sky News: "I have the support to run and resolve this impasse and I will do so if Jeremy doesn't take action soon."
Mr Corbyn's leadership is in crisis after 80% of his MPs called for him to step down and two-thirds of the shadow cabinet quit.
He is still attempting to fill shadow roles with the remaining MPs loyal to him.
But the shadow chancellor John McDonnell said Mr Corbyn was going nowhere, despite the threat of a leadership contest.