UK's Labour piles pressure on May over Brexit stance
May has ruled out staying in any customs union with the European Union after Brexit because it would prevent the country from striking its own new trade deals with fast-growing economies such as China and India.
In a speech, Corbyn is expected to indicate his party's support for agreeing a customs union, a decision that could result in the biggest test of May's fragile authority in parliament.
Supporters of Brexit have long said striking trade deals around the world would represent one of the big potential gains for Britain from leaving the EU.
If instead it stayed in a customs union with the EU, Britain could avoid tariff barriers for its exports to the bloc as well as the risk of a return to a so-called hard border between Northern Ireland and the Republic of Ireland, a prospect that alarms many in Dublin and Belfast.
Corbyn, a veteran left-wing lawmaker is expected to disappoint some politicians in his party by indicating he, like May, favours taking Britain out of the EU's single market.
"There will be some who will tell you that Brexit is a disaster for this country and some who will tell you that Brexit will create a land of milk and honey. The truth is more down to earth and it's in our hands: Brexit is what we make of it together," Corbyn will say, according to excerpts of the speech.
"Labour would negotiate a new and strong relationship with the single market that includes full tariff-free access and a floor under existing rights, standards and protections."
If Britain stayed in the EU's single market, it would have to continue accepting the free movement of people from the bloc, follow the rulings of its top court of justice and carry on contributing to the EU budget, something both May and Corbyn have ruled out.
Labour is currently ahead in opinion polls but, like the ruling Conservative party, it remains deeply split on its Brexit strategy as the clock ticks towards Britain's formal exit from the EU in March next year.
The party's divisions were exposed over the weekend when more than 80 senior figures in the party called on Corbyn to commit to remaining in the EU's single market.
Labour's Brexit policy chief Keir Starmer said on Sunday his party has agreed that if it wins power it would negotiate to remain permanently in a new customs union with the bloc, opening up a divide between the two main parties.
This could lead Labour to vote with Conservative members of parliament who are backing amendments to trade legislation that would keep Britain in a customs union.
Starmer warned that "crunch time is coming" for May and Labour would probably support the amendments.
Trade Secretary Liam Fox said the government would delay the key vote on the trade bill partly because it wanted more time to convince its own lawmakers to vote with the government.
May is due to set out her own vision for Britain's post-Brexit relationship with the EU in a speech on Friday. She hosted an eight-hour meeting of her top Brexit ministers last week in an attempt to forge a common position.