The party is keen not to lose its supporters, mostly in northern England, who backed Brexit and have been reticent on how they see the future relationship with the bloc.
In a speech in the Italian city of Florence, May will set out on Friday her vision for future ties with the European Union and try to fill an apparent policy vacuum.
Theresa May is rallying for support from fellow law makers on the EU withdrawal Bill.
Britain set out its determination to negotiate a tailor-made agreement to enforce its own laws and resolve disputes once it has left the bloc in March 2019.
May is trying to unite her party and shepherd the country through Brexit while facing calls to quit after losing majority in the snap elections she called.
The vote was moved by Corbyn’s Labour to get May to change her government’s austerity agenda and increase public spending, but May’s coalition won narrowly.
It was a clear attempt by May to reach more voters, some of whom may not tune into news programmes which are usually dominated by election news and the Brexit.
Beyond saying she will begin the formal process by the end of this month, May has yet to answer the question of exactly when, and end nine months of guesswork as to how her government will approach the unchartered territory of leaving the EU.
May, who is also under pressure from some of her lawmakers over her strategy for Brexit, has stuck to her commitment to a state visit for Trump this year.
Together with public comments by ministers in her Conservative government, the changes appear to suggest May is now supporting continued membership of the EU market if possible.
As the Opposition’s shadow cabinet is slowly dismantling, a motion of no confidence in Corbyn will be debated later this week.