It is thought that refusing to support this amendment would lead to more Labour defections to The Independent Group, deepening the party split.
"We are committed to also putting forward or supporting an amendment in favour of a public vote to prevent a damaging Tory (Conservative) Brexit being forced on the country", Corbyn will tell a meeting of his Labour lawmakers, according to extracts provided by his office.
It is unclear whether the Labour frontbench is prepared to table its own amendment for a second referendum or whether it will back one tabled by other parties or backbenchers.
"We're working with them to see can we have a redraft of that amendment which people could vote for".
But the delay has fuelled the theory that Mrs May is attempting to force the hand of MPs with the threat of a delayed Brexit unless her deal is accepted.
Earlier John McDonnell, the second most powerful man in the Labour Party, gave his strongest indication yet that Labour is close to backing a second public vote and said he would campaign for remain if one is held.
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He added: 'We will also be backing the Cooper-Letwin amendment to rule out a No Deal outcome.
Asked to clarify if he was considering calling for another referendum, Corbyn said: "That's the point we're discussing now in the party". One way or another, we will do everything in our power to prevent no deal and oppose a damaging Tory Brexit based on Theresa May's overwhelmingly rejected deal. Jeremy Corbyn is today taking the first step to reunite our party by showing he is listening to our voters and members on this, the biggest issue of our time.
'Last week, after our visit to talk to European Union officials and leaders in Brussels and Madrid, no one can be in any doubt Labour's alternative Brexit plan is serious and credible'.
'To my mind we would never have been forgiven for facilitating Tory Brexit'.
"We have to deal with these people, and I think it is a responsibility of everyone in the Labour Party, from the top to the bottom, to report cases", he said. But supporters of a second referendum say it is the only way to break the deadlock in parliament by asking for the people to decide.
"If our new independent splitters have got the guts to have by-elections, we will crush them".