Robert Cate explains that Deutero-Isaiah seems to be unknown to Jeremiah.
Robert L. Cate, "Isaiah, Book of," Mercer Dictionary of the Bible (United States: Mercer University Press, 1990) 413-415
In addition to this internal evidence from the book of Isaiah, the Bible twice refers to the edict of Cyrus that allowed the Jews to return home from Babylon as being in fulfillment of the prophecy of Jeremiah (2 Chr 36:22-23; Ezra 1:1-4). Such a reference to Jeremiah's prediction of a return from exile after seventy years is surprising if a direct reference to Cyrus by name had been available from the preaching of Isaiah. Further, Jeremiah only barely escaped death following his prediction of the destruction of the Temple (Jer 7:26). That he was delivered at all was due to the discovery of a one-verse reference in the prophecy of Micah (Mic 3:12). This entire episode becomes difficult to understand if the material in Isa 40-66 had been available, for it presupposes the destruction of the Temple (44:26, 28; 49:10; 51:17-20; 52:9; 60:10; 63:18; 64:10-11). The people of Jeremiah's day showed no awareness of any of these passages.