This article doesn't really say. It mentions he was trying to end the war which was costing up to $2 million per day, but how ending slavery in non-Confederate states would accomplish that isn't mentioned.
I'm trying to recall what I've read previously. My guess would be that if the states in question went along, he could show the Confederate states a workable plan that might bring them to the table. I believe Lincoln was willing to try almost anything to reduce the suffering. 'Almost' is the operative word.
Well he finally did end the suffering by giving Grant and Sherman the go-ahead to "press the issue".