The Public Policy Polling survey released Wednesday found that just 27 percent of Texas Republicans think Cruz would be the best GOP candidate to run for president. 

But that's still more than other politicians PPP listed. Eighteen percent of Texas Republicans want Texas Gov. Rick Perry (R) to run for president again in 2016 and just 15 percent of the state's Republicans picked former Florida Gov. Jeb Bush (R). New Jersey Gov. Chris Christie (R) and Sen. Rand PaulRandal (Rand) Howard PaulCongress must end American support for Saudi war in Yemen Black men get longer prison sentences than white men for same crimes: study Sarah Palin on sexual harassment: 'People know I'm probably packing' so they 'don't mess with me' MORE (R-Ky.) got 11 percent support, respectively among Texas Republicans to run for president.

Publicly, Cruz has deflected suggestions that he is planning to run for president in 2016. But in May, National Review, citing close friends and confidantes, said the junior senator from Texas had begun mulling running for president.

The PPP poll is not the first survey that found Cruz as the preferred presidential candidate among Texas Republicans. In June, a University of Texas/Texas Tribune poll found 25 percent of Texas Republicans would vote for Cruz if the Republican presidential primary were held today, more than any other potential candidate listed.

The PPP poll was conducted among 500 registered voters and 318 Republican primary voters. The poll was done June 28 to July 1 and had a margin of error of plus or minus 4.4 percentage points statewide and 5.5 percentage points for the Republican primary questions.