The issue will be discussed at a meeting of the General Synod this weekend and has caused a split in the church.
Bishop of Oxford, Steven Croft, is among those pushing for the church to start disinvesting from companies not acting quickly enough to combat climate change from 2020.
He told the BBC: "The world is facing catastrophic climate change. From 2020 we must not be investing in fossil fuel companies which are burning oil and gas which should be left in the ground.
"It's fine if they have plans for the orderly transition in line with Paris, we shouldn't universally pull out of fossil fuels, but we mustn't be profiting from companies which are not keeping to the Paris agreement.
"We have not yet seen from the fossil fuel companies... sufficient change.
"If their profits depend on burning fossil fuels which the Paris agreement says should be unburned then the church should not be investing in them."
However, Bishop of Manchester David Walker said it was better for the church to use its influence as a shareholder to push a green agenda rather than to pull out of companies.
He said: "We got over 60% of the votes at the ExxonMobile, a big, traditional, fairly macho, American oil company, to vote in favour of our shareholder resolution in New York a few months ago. And that company is having to make changes now.
"We think we can get a good number of these companies in the next few years to come into line with the Paris agreement.
"We don't think we can do it quite by 2020. I think we're really discussing, not the principle, but the date.
"It takes a while to turn around an oil tanker, and that's what we are trying to do."
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