Kris Kobach said Tuesday he is eager to become President Trump's Homeland Security secretary and confirmed he has been communicating with the White House about the job.

Kobach is emerging as the favorite of immigration hawks as Trump considers replacements for Kirstjen Nielsen. The former Kansas secretary of state, a Trump confidant on immigration matters, built his political career around advocating for curbing immigration into the United States, whether legal or illegal.

After the president fired Nielsen for, in his view, not cracking down on the flow of illegal migration across the Mexican border in a show of strength ahead of 2020, immigration restrictionists are hoping Kobach gets the nod — despite warnings from establishment Republicans that Senate confirmation would be an uphill battle.

"He’s got an important decision to make," Kobach said of Trump, in an interview with the Washington Examiner. "If he wants to have me serve in this capacity, and thinks it would be the best thing for the country, I would certainly do so."

[Related: GOP Kansas senator says no-go on Kobach for homeland security secretary: 'We can’t confirm him']

On Tuesday, Numbers USA, a group that staunchly opposes illegal immigration but also advocates for reducing legal immigration, urged Trump to replace Nielsen with Kobach. "Kris Kobach is, without question, the best choice to lead DHS, and we hope he will be President Trump’s nominee," the group said in a statement. "He is committed to the President’s promise to ensure that immigration serves the interests of America and American workers."

Kobach, 53, was headed to New Mexico Tuesday to survey land for the construction of a border wall as part of his work for "We Build the Wall," a group that seeks to harness private money to build Trump's wall by purchasing privately owned land along the southern border from willing sellers. Kobach, a Republican, lost his bid for Kansas governor in 2018, but has been mulling a campaign for Senate to succeed retiring Sen. Pat Roberts, R-Kan.

He said he would not be a candidate for Senate if he were picked to run the Homeland Security Department, which oversees all aspects of U.S. immigration enforcement.

White House officials, who requested anonymity to discuss personnel issues, have played down suggestions that the rash of departures at Homeland Security were connected and said any permanent head of the department would be expected to continue the president's focus on immigration.

[Also read: Border Patrol leader says 'caravan-equivalent numbers of migrants' reach southwest border 'every seven days’]

Rob Crilly contributed to this report.