The poll asked: "Regardless of who you support, please tell me whether you would or would not like to see each of the following people run for the Republican nomination for President." The respondents were then asked about Ryan, Christie, Perry and Bush.
Forty-eight percent said they would like to see Ryan run, 45 percent said they would like to see Christie run, 40 percent said they would like to see Perry run and 39 percent would like to see Bush run.
Ryan also had the fewest Republicans saying they would not like to see him run.
Fifty-eight percent of the Republicans polled said they would not like to see Jeb Bush run, 50 percent said they would not like to see Perry run, 45 percent said they would not like to see Christie run, and 43 percent said they would not like to see Ryan run.
Ryan has garnered attention in recent weeks as author of The Path to Prosperity, the budget plan approved by the Republican-controlled House of Representatives. The plan would cut federal spending over ten years by $6.2 trillion compared to the budget proposed by President Barack Obama.
The Ryan budget plan would also convert Medicaid into a block grant program for states and would reform Medicare so that the current system is preserved for all Americans 55 and over but that younger workers would get a subsidy for insurance premiums when they retire so that they could choose and purchase their own guaranteed health-care plan.
The CNN/Opinion research poll surveyed 473 Republicans nationwide from May 24-26.