"Mike Pompeo is not somebody that's not going to back down to these terrorists that are out there, these dictators that are out there", Arnold says.
In October, Tillerson shot down a report that said he had been on the verge of resigning from his Cabinet position over the summer.
The nature of the reported change also suggests a change in the administration's focus, with Tillerson having, for instance, ruled out imposing regime change in North Korea, while Pompeo, said to be a Trump favorite recently, has openly advocated it.
But White House spokeswoman Sarah Huckabee Sanders didn't deny it.
That followed a tweet by Trump that Tillerson should not waste his time by seeking negotiations with North Korea over its nuclear and missile programme, widely seen as a sign of the secretary of state being marginalized. Both Republican Sen. Tom Cotton of Arkansas and retired Navy Vice Adm. Robert Harward are under consideration for that post.
"I think he has represented the United States' interests exceedingly well, particularly in our region", she told Sky News on Friday.
A source familiar with Tillerson's thinking said the secretary of state's original plan when he took the job was to leave in February.
Tillerson has embittered many in the State Department by embracing the planned budget cut, failing to get top officials into key diplomatic jobs, relying on a handful of aides and keeping his distance from career diplomats.
But the White House's tentative plans to replace Pompeo at the Central Intelligence Agency with Sen.
Observers across the political and foreign policy spectrum tend to view Tillerson as a failure at the State Department.