Voters in Kentucky do not know enough about Sen. Rand PaulRandal (Rand) Howard PaulDem wins Kentucky state House seat in district Trump won by 49 points GOP's tax reform bait-and-switch will widen inequality Pentagon budget euphoria could be short-lived MORE (R-Ky.) to say if they would like to see him run for president in 2016. 

According to a New York Times-Kaiser Family Foundation poll released Wednesday, only 31 percent of voters there would like to see the freshman senator run for president. 

Another 34 percent say they would not, while 32 percent say they do not know enough about him to say. 

Paul, who is considering a run, has recently been near the front of the pack nationally in early polling of the GOP presidential primary. 

A majority of voters in Kentucky, however, do approve of the job Paul is doing in the United States Senate. Fifty-three percent approve, while 34 percent disapprove. Another 14 percent do not know. 

His approval rating is 13 points higher than Kentucky's other senator, Senate Minority Leader Mitch McConnell. 

It is not uncommon for state voters to say they do not want to see their own lawmaker run for president. A recent Quinnipiac poll showed only 43 percent of New Jersey voters would like to see Gov. Chris Christie (R) run for president. That number was largely unchanged from last year, when he garnered high approval ratings. 

The New York Times poll surveyed 900 registered voters in Kentucky and has a 4-percentage-point margin of error.