Amidst the speculation over Cook and Peary, Amundsen told reporters, somewhat disingenuously, "It would be useless to make speculations as to the points arrived at by the two explorers. It is not important if the exact mathematical pole was reached or not, but it is important that the geographical conditions of the spot were observed. Probably something will be left to be done. What is left will be sufficient for all of us." 
He was on his way to Copenhagen to see Cook, who was being fêted as "the conqueror of the North Pole". He had left a note for Leon, "Write to Thv. Nilsen ... and tell him the exp. is postponed and will get under way in a few months.... Give the same reason to all the others. Possible departure July 1910." 
Some years later, Cook wrote of their visit, "Amundsen told me ... that he was about ready to take the Fram ... for another try at the Pole. He asked me about the currents, the weather, and what I thought of the prospects. I advised against the execution of the enterprise because at best I believed he could only duplicate the voyage of Nansen and Sverdrup. Furthermore, I said the North Pole is now out of the picture. Why not try for the South Pole.... [The idea] almost took Amundsen's breath."
Whether or not Cook was in fact the first to suggest the South Pole to Amundsen is not known, or if Amundsen's surprise was due to Cook inadvertently lighting on his change of plan.
"He sat in meditation for a while as was his custom when new ideas were suddenly flashed. Then said Amundsen, 'The Fram is not a good sea boat for the heavy South Seas. But this is the thing to do. Let me think it over.'" 
Amundsen himself wrote afterwards, "Just as rapidly as the message had travelled over the cables I decided on my change of front -- to turn to the right-about, and face to the South." 
 New York Times, 8 September 1909, quoted by Roland Huntford in Scott and Amundsen (New York : Putnam, 1980, c1979), p.216.
 Roald Amundsen, note to Leon Amundsen, [ca. 7 September, 1909], quoted by Tor Bomann-Larsen in Roald Amundsen (Stroud, Gloucestershire : Sutton, c2006, c1995), p.75.
 F.A. Cook, unpublished memoirs, quoted by Roland Huntford in Scott and Amundsen (New York : Putnam, 1980, c1979), p.216.
 Roald Amundsen, The South Pole, ch.2.