Not Lincoln or Grant, but Sherman-----

From Sherman's memoirs---

CHAPTER XIX.
CAPTURE OF ATLANTA.

AUGUST AND SEPTEMBER, 1864

"Soon after our reaching Atlanta, General Hood had sent in by a flag of truce a proposition, offering a general exchange of prisoners, saying that he was authorized to make such an exchange by the Richmond authorities, out of the vast number of our men then held captive at Andersonville, the same whom General Stoneman had hoped to rescue at the time of his raid. Some of these prisoners had already escaped and got in, had described the pitiable condition of the remainder, and, although I felt a sympathy for their hardships and sufferings as deeply as any man could, yet as nearly all the prisoners who had been captured by us during the campaign had been sent, as fast as taken, to the usual depots North, they were then beyond my control. There were still about two thousand, mostly captured at Jonesboro, who had been sent back by cars, but had not passed Chattanooga. These I ordered back, and offered General Hood to exchange them for Stoneman, Buell, and such of my own army as would make up the equivalent; but I would not exchange for his prisoners generally, because I knew these would have to be sent to their own regiments, away from my army, whereas all we could give him could at once be put to duty in his immediate arm"