Lankford, R-Oklahoma City, declined early Sunday afternoon to comment.
Also, the sources said, Oklahoma Corporation Commissioner Patrice Douglas and state Sen. Clark Jolley — both Republicans from Edmond — are expected to announce their intentions to run for Lankford's seat, which includes most of Oklahoma County and Pottowatomie and Seminole counties.
Lankford, 45, has been in the U.S. House since 2011 and has risen quickly, winning a leadership job — chairman of the Republican Policy Committee — after his first term. The former Baptist church camp director also has been an active chairman of a House oversight subcommittee; he was a heavy favorite to win a third term this year.
He had about $455,000 in his campaign account at the end of October; a report that runs through Dec. 31 is due soon. He can use money in that account for a Senate race.
Lankford has a town hall meeting scheduled for 6 p.m. Tuesday at the Metro Technology Center in Oklahoma City.
Freshman Rep. Jim Bridenstine, R-Tulsa, also is considered a possible contender for Coburn's seat. A spokeswoman for Bridenstine declined to comment Sunday on Bridenstine's timetable for making a decision.
U.S. Rep. Tom Cole, R-Moore, announced Sunday that he's no longer looking at the Senate race; Cole is rapidly gaining influence on the House Appropriations Committee and he's a close ally of House Speaker John Boehner, R-Ohio.
“My seniority, my membership on three major committees, my position as a subcommittee chairman on the Appropriations Committee and my role as a deputy whip in the Republican Conference make me much more valuable to Oklahoma and the 4th District in the House than I could be as a freshman U.S. senator,'' Cole said.
Oklahoma Attorney General Scott Pruitt also bowed out of the race.
“Perhaps there will be a day in the future when the need for my service and leadership shifts elsewhere,'' Pruitt said. “Then, it will be time to alter my focus but that time is not now.”
Coburn, R-Muskogee, announced Thursday night that he will resign after the current congressional session, foregoing the final two years of his term.
Gov. Mary Fallin has announced that the special election for the last two years of Coburn's term will run parallel to the already scheduled elections.
That means candidates will have to run a statewide campaign on a very compressed time frame; the primary is only about six months away, on June 24.
Douglas, whose seat on the Corporation Commission is on the ballot this year, must choose between running for re-election or running for Lankford's seat.
Douglas said Sunday that she is “going to consider the opportunity” to run for Lankford's seat. She said she and her husband and children were “huddled as a family” and were talking and praying about it.
Jolley was re-elected last year and would not have to give up his Senate seat to run for Lankford's House seat.
Jolley said Sunday, “Congressman Lankford has been a fantastic member of the U.S. House and I think he would be an outstanding senator. My family and I are talking about the unique opportunity such a race would present.”