hot on the scent (or trail) of. In close or intense pursuit of something being chased of tracked, or near to the discovery of something concealed.

Reporters, detectives, bounty hunters, treasure hunters, and searchers and investigators of all kinds would like to be and are likely to be depicted as hot on the scent or trail of something. That is, almost ready to find it, really, really close behind, or excited about the prospects of catching. The difference between being “hot on the scent of” and “hounding” or “dogging” is that in this case the pursuer does not yet know where the prey is, though s/he does have clues (figurative scents) to follow. In comparison, “sniff out” emphasizes the process of discovery but not the pursuit.

The New York Times described fashionista Dimitri Viglis as “hot on the scent of the new, the colorful, the inventive and the rare” as he trolled street-wear shops in lower Manhattan. A few years earlier, they were glad to make a pun of it when discussing research by the Defense Advanced Research Projects Agency on “a sniffing machine that can detect individuals by their body odor.” Reporter Nicholas Wade's lead for the story was: “Hot on the scent of a suspected terrorist?” Terrorists seem especially amenable to being described as hotly trailed. Paul Berman wrote hopefully in March 2003 that “Police agents, as I write, seem to be hot on the trail of bin Laden himself...”

The Oxford English Dictionary cites Albion Tourgée's A Fools' Errand (1897): “A pack of hounds running on a hot trail.” In this case, the editors believe that “hot” refers to the strength or freshness of the scent. They go on to note that “in nursery and parlour games which involve searching or guessing on the part of some of the players, hot means close on the track of the object hidden or the solution to be guessed”