Koppel is leaving the network and his signature show in December.
"We're looking forward to ushering the new 'Nightline' in the new season," an ABC News spokesman said Tuesday. "But at this point, we have nothing to announce. We understand people will speculate on little or no information, but when we have an announcement, we will make it widely known."
The Post quoted sources saying the new "Nightline" will keep its Washington roots, but will also broadcast occasionally from New York.
Of the finalists, McFadden is co-anchor of "Primetime," Moran is the network's chief White House correspondent and Bashir joined "20/20" in 2004.
The British journalist is best known for his "Living with Michael Jackson" documentary, during which the pop star admitted sleeping with young boys.