Former state Republican Party Chairman Chris DePino is considered the strongest potential Senate candidate his party could field but has yet to announce a decision about running.
Dodd had served in the Senate since 1980. Although he is pondering a run for the Democratic presidential nomination, it is likely he will run for re-election.
Dodd won 65 percent in his 1998 re-election race against former 5th district Rep. Gary Franks.
Departure Official, Vote For Combest Seat Is Set
Rep. Larry Combest (R) officially tendered his resignation to Gov. Rick Perry (R) on Tuesday.
In a letter to Perry, Combest wrote that "there comes a time in everyoneís life when the focus needs to be more on family than on other things and I am at that point in my life."
First elected to the West Texas 19th district in 1984, Combest regularly won re-election with ease and had risen to the chairmanship of the House Agriculture Committee.
Perry is expected to set a May 3 special election to choose Combestís replacement.
A gigantic field of Republican candidates has already emerged.
Among the Republicans given a real shot of winning the seat are: state Rep. Carl Isett, former Lubbock City Councilman Randy Neugebauer, Midland businessman Mike Conaway and former Midland Mayor Carroll Thomas.
Only one Democrat, former newscaster Kaye Gaddy, has announced for the race.
The seat heavily tilts toward Republicans, as Bush would have won the seat with 76 percent of the vote in 2000.
Following the speeches from elected officials, the crowd stands at long tables as they dig into BBQ, brunswick stew, cadillac rice at the Law Enforcement Cookout at Wayne Dasher's pond house in Glennville, Ga., on Thursday, April 17, 2014.