A final vote will take place on Monday, two years after the previous measure failed to pass because it fell six votes short of the required two thirds majority among lay members, despite being backed by almost three quarters of the synod.
However, many observers expect the vote to pass on this occasion after efforts were made to cater for some traditionalists who remain largely opposed to women holding positions of authority within the Church.
As part of the new terms, the House of Bishops have introduced five guiding principles including the installation of an ombudsman who would settle any potential diocesan disputes between any women bishops and traditional anglicans.
The new measure has been well received after 90 percent of clergy from all 43 dioceses approved the new terms of the draft legislation in principal in February.
The Secretary General of the Church of England's governing body, William Fittall, has also said there would be "shock and bemusement" if the synod fails to appove the introduction of women bishops on this occasion.
But Revd Jody Stowell from pro-women bishops campaign group WATCH has been impressed by how fast the legislation has been returned to the Synod, she said: "the speed in which this legislation has come, off the back of it failing last time is actually pretty miraculous. So, we're very hopeful that actually this is really where people want us to be and this is what they want to happen."
Meanwhile, Church of England clergy are likely to be banned from joining the BNP or National Front after Friday's General Synod.
Elsewhere, the money-making arm of the Church of England has said it's doing "all it can" to avoid unethical investment after severing ties with Wonga.
The Church Commissioners for England have admitted they were embarrassed last year when it emerged money was indirectly invested in the firm.
Reacting to the development, David Barclay who has campaigned against payday lenders and is part of the Church's credit union project said: "I think it's really important now to be able to give a very clear answer to the grass roots level [of the church], so that people can see when the Church says something it follows through with it."
Last year, the Archbishop of Canterbury accused the firm of exploiting the poor, before it emerged hours later the church had an indirect investment in it.
However, in June, the Archbishop of Canterbury appeared to have toned down his approach to payday lenders when he suggested shutting them down could leave the poor in the hands of loan sharks.
At a lecture in Westminster, Most Revd Justin Welby warned putting such firms out of business before an alternative is in place could make things worse.
Hear more from David Barclay here: