Labour's new amendment is being touted as an alternative to the EEA amendment, which was recently passed in the House of Lords and will be presented to the Commons on Tuesday 12th June.
Labour will formally abstain on the EEA amendment but will vote in favour of the other 14 changes in a bid to defeat the government.
Potential splits among Labour's MPs caused by the move reduce the chances of a defeat for the Prime Minister.
"Labour will only accept a Brexit deal that delivers the benefits of the single market and protects jobs and living standards", said Keir Starmer, Labour's Brexit policy chief.
Unlike the Tories, Labour will not sacrifice jobs and the economy in the pursuit of a reckless and extreme interpretation of the referendum result.
The government says the United Kingdom must leave the EU's single market.
"Two years on from the referendum it is clear that the government has no plan for how it will protect jobs and the economy, and guarantee no hard border in Northern Ireland".
A journalist for The Times newspaper tweeted a letter from the top official responsible for making sure lawmakers in the ruling Conservative Party vote in support of the government, asking them to make sure they will be working in parliament on that date.
And Labour MP Chuka Umunna, a supporter of the pro-EU Open Britain campaign, said Mr Corbyn's proposal was "a fudge" and "nowhere near enough".
"Labour's amendment, along with a commitment to negotiate a new comprehensive customs union with the EU, is a strong and balanced package that would retain the benefits of the single market".
"This amendment means accepting free movement and continuing to follow European Union rules with absolutely no say in them, which is the worst of all worlds".
The Lib Dems accused Labour of "peddling snake oil in a bottle wrapped with the EU" with their amendments, insisting the only way to access the Single Market is to be part of the EEA.
Some 81 per cent of those who backed Leave in 2016 said they still believed it was the right decision, with nine per cent now saying it was wrong.