Initially, Trump seemed to have settled on Texas Rep. Mike McCaul – telling Gen. Kelly at one point to “hire him.” But he was recently ruled out of contention after vocal objections from Attorney Gen. Sessions and other immigration hardliners inside the White House who thought McCaul was not tough enough on immigration issues.

In addition, acting Secretary Duke is considered unlikely to be appointed the permanent director, and is currently not an “active contender,” sources say. However a senior DHS official emphasized that there is no real pressure to name a new secretary right away because she’s done a good job thus far leading the agency.