Jindal, who was re-elected as governor in 2011 for a second four year term, is term-limited that is he cannot contest for the State's top job again.
The Republican survey, conducted last week also found President Barack Obama's approval rating as 37 percent in the state, according to the Politico, an influential Washington news site that focused on politics.
The poll found that 55 percent Louisianans support Jindal's controversial decision not to expand Medicaid, a US government health programme for families and individuals with low income and resources, with 37 percent opposed.
Four-fifths of Republicans also favour his Medicaid position.
The poll also found that 62 percent of Louisianans oppose Obama's signature healthcare law, nicknamed Obamacare, that aims to increase the quality and affordability of health insurance in US, 53 percent strongly so. Only 33 percent favor the law.
OnMessage Inc., Jindal's main consulting firm, surveyed 800 voters from Aug 12 to 15 for the National Republican Senatorial Committee, Politico reported.
The results were weighted to reflect historic turnout trends. The margin of error is plus or minus 3.5 percentage points.
The Washington Post previously reported their finding that Democratic Senator Mary Landrieu leads Republican front-runner House member Bill Cassidy by 4 points, 45 percent to 41 percent. Cassidy was up among independents by 4 points, 41 percent to 37 percent, according to Politico.
Landrieu voted for the 2010 health care overhaul.