"I have been contacted by a number of people and organizations around the country asking me to consider it," he said when asked whether he is keeping the door open to a run.
But he added that he isn't yet reaching out to people to ask for their support, and said he'd like to wait to see who jumps into the race before he decides.
"I'm not going to make the mistake of making any decisions before I know who the players are," he said.
Kirby flirted with a run against Johnson in 2008 but eventually declined. The former lieutenant governor lost a 2002 gubernatorial bid to Republican Mike Rounds in the primary, and Rounds went on to win the seat.
Rounds is currently the only player officially in the race. He formally launched his campaign late last year, before Johnson had made his decision to run.
But Rounds has faced criticism that he's not conservative enough, and could see a challenge for the Republican nomination. The Senate Conservatives Fund, a PAC that has backed conservative candidates in GOP primaries, is looking for a "true conservative" alternative.
Rep. Kristi Noem (R-S.D.) could be that alternative, and is looking at the seat, but an SCF spokesman was lukewarm when asked about her conservative credentials.
Kirby, who is treasurer for Noem's leadership PAC, said he wouldn't enter the race if she did. He said, however, that the decision of state Sen. Larry Rhoden (R), who is also looking at the race, wouldn't affect his choice.
Democrats are looking at a potential primary between former Rep. Stephanie Herseth Sandlin and U.S. Attorney Brendan Johnson, the son of Sen. Johnson.