There is a widespread expectation that the deal will be signed on Friday, though the timings are uncertain.
Delegates worked through Thursday night on a draft version to iron out the key barriers to an agreement.
French Foreign Minister Laurent Fabius, who is chairing the summit, told negotiators: "I think we will make it."
Participants at COP21 - as the UN conference is called - have been working on a draft text, prepared by the French presidency, since Wednesday.
This was seen as a significant moment after discussions that began in 2011 about a new global agreement that would stake out a long-term strategy for dealing with climate change.
Any deal signed here in Paris would come into being in 2020.