Cochran has said he will make a decision by the end of the month.
Childers said he would be "less apt" to run if Cochran does, though he declined to rule it out. He sounds as though he would attempt to appeal to Cochran supporters, calling it "kind of odd" that McDaniel got into the race before Cochran's announcement.
"Probably nobody within the state of Mississippi has more respect for (Cochran) than I do," Childers said.
Childers, a Blue Dog Democrat, would likely need to benefit from a hard-fought GOP primary and/or a wounded GOP nominee. Moderate and Blue Dog Democrats have won a number of Senate races in recent years thanks to GOP infighting and flawed nominees.
A fellow Blue Dog, then-Rep. Joe Donnelly (D-Ind.), won his seat in 2012 after Richard Mourdock upended longtime Sen. Richard Lugar in the Indiana GOP Senate primary. Similarly, Sens. Claire McCaskill (Mo.), Jon Tester (Mont.) and Heidi Heitkamp (N.D.) defeated flawed GOP nominees in states that Mitt Romney easily carried in the 2012 presidential race.
Childers was one of three Democrats to steal a conservative-leaning House seat in a series of 2008 special elections, and at the time he was hailed as the kind of candidate who could reclaim parts of the South for Democrats. But he was defeated by 14 points in the GOP-dominated 2010 election by now-Rep. Alan Nunnelee (R-Miss.).
Since then, the former Prentiss County chancery clerk has focused on his real estate business.
Mississippi has gone between 55 and 60 percent for the last four GOP presidential nominees. President Obama managed 43 percent and 44 percent of the vote there in 2008 and 2012, respectively, thanks in large part to increased turnout among the state's African American population. (The state is 37 percent black.)
Getting such favorable African American turnout in a midterm election without Obama on the ballot, though, will prove difficult.
Democrats last made a run at a Mississippi Senate seat in 2008, when former governor Ronnie Musgrove (D) fell to appointed Sen. Roger Wicker (R) by 10 points.
Other Republicans who might be interested if Cochran retires include Mississippi Secretary of State Delbert Hoseman, state Auditor Stacey Pickering, Rep. Gregg Harper and Lt. Gov. Tate Reeves.