"I have not had any conversations directly with the White House yet on this," Steele told C-SPAN.
Ken Mehlman, the current chairman, is stepping down when his two-year term ends in January. Mehlman made a point of emphasizing outreach to black voters and helped recruit Steele for the Maryland race.
Steele, who lost to Democratic Rep. Benjamin Cardin by a margin of 55 percent to 44 percent of the vote, said he believed it was time for the GOP to rethink its views in wake of losing both chambers of Congress in last week's midterm elections, which he described as a "tsunami." Steele said the electorate "was very clear."
"They expected the administration and the party to step up and speak to particular issues and, failing that, there would be heck to pay — and we paid," Steele said.
Steele said he wasn't sure when an announcement would be made on who will be the new committee chair.
Steele was head of the Maryland Republican Party before being elected lieutenant governor in 2002 as the first black candidate elected statewide in Maryland. His term as lieutenant governor will end in January.
Steele also explained why he largely avoided mentioning his party affiliation while campaigning. In a state where registered Democrats outnumber Republicans 2-1, Steele said it was obvious what party he belonged to and there was no need to "rub it in your face."
"In a state like Maryland, there was an opportunity to move away from the labels and really try to dig beyond, you know, being a Republican or Democrat, red state or blue state," Steele said. "In fact, that's what people are sick of. I think we saw the results on Tuesday just how sick they are."