Corbyn could have swung some support behind May but another referendum would just set up more months of acrimony and I'm not sure a "remain" vote would settle it.
"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", Labour leader Corbyn was due to tell a meeting of his lawmakers on Monday, his office said.
No date has been set for the next round of votes, but Theresa May has said that she will put her Brexit deal to the vote on 12 March.
Shadow Brexit Secretary Keir Starmer said on Twitter: "This week Labour will put its alternative plan for a vote in the House of Commons".
Corbyn appears to support a second referendum on Brexit in a big shift for the opposition leader.
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The Labour leader, who has been a long time opponent of the European Union but has lost a number of MPs in the past week over his Brexit stance is expected to say: "The prime minister is recklessly running down the clock, in an attempt to force MPs to choose between her botched deal and a disastrous no-deal We can not and will not accept... one way or another, we will do everything in our power to prevent no deal".
Corbyn said he would work to force May to adopt his party's approach to Brexit, which includes a permanent customs union with the EU (a major sticking point between the pro- and anti-Brexit sides), a close alignment with the single market and unambiguous agreements on future security arrangements.
"It is welcome news that the Labour Party is now, at long last, signalling it will accept the principle of giving the public the final say on Brexit", he said. One possibility is that Labour will back the so called Kyle/Wilson compromise, an amendment being promoted by two Labour backbenchers Peter Kyle and Phil Wilson. "I think it's going to be deeply divisive", he said. MP David Lammy said that it would be "wrong" to force Brexit on the public in the current circumstances and that "any deal will be worse than the one we've already got inside the European Union". It is thought that refusing to support this amendment would lead to more Labour defections to The Independent Group, deepening the party split.
Crucially, if this amendment is not passed, then the party will push forward for another referendum of Britain's European Union withdrawal. When asked about the amendment, a Labour source repeated that the party "would not vote for a damaging Tory Brexit".
"And basically we are doing as instructed by Labour Party conference".