(CNN) - A new poll indicates about a third of Kentucky voters want their home-state senator, Rand Paul, to run for president, while another third want him to stay out of the 2016 race.
According to a New York Times/Kaiser Family Foundation survey released Tuesday, 31% of registered voters in the Bluegrass State say "yes" to a Paul presidential bid, compared to 34% who prefer the first term senator to avoid the presidential horse race.
Follow @politicalticker Follow @KilloughCNN
Another third (32%) say they don't know enough about the first-term senator to give an opinion. Three percent are undecided.
Paul, who's been aggressively building his national profile, says he'll wait until after the November midterm elections to make his decision. His name has topped some recent 2016 Republican presidential nomination polls as he seeks to broaden his appeal to more mainstream Republicans.
"It's better than placing at the bottom of those polls," Paul joked Tuesday while speaking at the University of Chicago's Institute of Politics.
On job approval ratings, 53% of Kentucky voters say they approve of the way Paul is handling his role as senator, while 32% disapprove and 14% have no opinion.
It's a different story for the senior senator from Kentucky. Republican Senate Leader Mitch McConnell's approval ratings are underwater, with 40% approving his actions in Congress, while 52% disapprove and 8% don't have an opinion.
That's not the best news for a longtime incumbent senator who's running for re-election this year and faces challenges from both the right and the left.
If McConnell makes it to the general election, the survey indicates McConnell would be in a statistical tie with likely Democratic nominee Alison Lundergan Grimes, 44%-43%.
For the survey, 891 registered voters in Kentucky were interviewed by phone from April 8-15. The sampling error is plus or minus four percentage points.