What is the context of Lincoln saying: "if I could save the union without freeing any slave I would do it"

The most important context is provided by the surrounding paragraph:

I would save the Union ... If there be those who would not save the Union, unless they could at the same time save slavery, I do not agree with them.

If there be those who would not save the Union unless they could at the same time destroy slavery, I do not agree with them.

My paramount object in this struggle is to save the Union, and is not either to save or to destroy slavery.

If I could save the Union without freeing any slave I would do it, and if I could save it by freeing all the slaves I would do it;

and if I could save it by freeing some and leaving others alone I would also do that. What I do about slavery, and the colored race, I do because I believe it helps to save the Union;

and what I forbear, I forbear because I do not believe it would help to save the Union.

Lincoln wanted to reassure his fellow country-men that above all, he valued the union above all else; and to that end, he mentions in this short paragraph the term 'Union' seven times.

Though he personally believed that slavery was an evil abomination and required abolishing, yet he was willing to 'forbear' for the sake of the union; but as it turned out, not for all time; but for the time it took for him to marshall his forces, and to fortify them.

Lincoln's personal feelings about slavery aside, his policy has to reflect the collective will of his constituency and in particular the union bourgeoisie that financed his campaign and the war. The union bourgeoisie could care less about slavery but preservation of the union was essential for efficient exploitation of resources within the then current boundaries and also ordered western expansion of boundaries and legal claims all the way to the west coast. The spoils of war would also for the most part go to the backers and financiers of the war's victors. Who received most of the contracts for reconstruction of the south? http://www.encyclopedia.com/history/united-states-and-canada/us-history/reconstruction

Back then as now, the sometime paradoxical political utterances from the top politicians can be better understood by asking "qui bono" (who benefits) from the outcome of the underlying policy being pursued.

Everybody knew that Slavery was on a dead branch of the American family tree. The North knew it. Lincoln knew it. The south knew it, that's why they seceded. It had no future in the Union. That wasn't Lincoln's doing, It was the Kansas Nebraska Act which cut off slavery from growing or even keeping pace politically with those who would oppose it. It was the Dred Scott decision, which made it so the more populous and economically successful north could no longer ignore slavery as now it was on their doorstep. And it was 90 years of constant struggle in the Senate which had exasperated the opposition party into reforming itself as an abolitionist party. Lincoln who was an abolitionist, was willing to let slavery die a protracted political death of 1000 cuts, if he could avoid a civil war. It would be a terrible thing if slavery lasted another 10-20-40 years, but if a civil war which killed 600-800,000 men could be avoided, Lincoln would try to avoid the war. He wasn't bargaining on ending slavery, he was bargaining on the timing.

Which leads to the question why did Lincoln go to war, certainly not because of slavery. The only thing worse than a Civil war would be to allow the south to secede. Succession itself was the cases belli of the civil war as far as the North was concerned. That's all the justification which Lincoln required to go to war. The founding fathers from the north and south through Federalist Papers #6-10 warned that if the United States fractured, America would be condemned to fight 1000 years of wars as Europe had experienced. Two nations similarly suited would compete religiously, culturally, geographical and economically; all of which lead to War in the European experience. That is what Lincoln was even willing to go to war to avoid...

Now once he was at war and had paid that great price, he made damned sure he got slavery finished off too. Which was his personal belief, the platform his party was created to accomplish, and the platform he personally was elected to pursue.

Horace Greeley was a "Radical" Republican, whose primary interest was the freeing of the slaves. In this, he differed from "mainstream" Republicans who were driven by economic interests (pro business, pro free labor, pro free soil).

Lincoln was basically "agnostic" on the question of freeing the slaves, or the African-American question generally. His response to Greeley was addressed the fact that Greeley represented only a small percentage of Republicans, and that Lincoln might be able to manage without his "faction." As it turned out, he couldn't, so Lincoln promulgated the Emancipation Proclamation. People who shared Greeley's views didn't number "twenty million" but were numerous enough to make a difference.

Basically, the exchange offered Greeley an opportunity to "declare victory and go home." His stance after the Emancipation Proclamation was, yes, Lincoln was "bargaining" with his statement, but he eventually came around.