His presence at the four-day convention with an important speech has triggered renewed speculation that he will be the vice presidential candidate for the party. John McCain is expected to be nominated at the convention as the party's presidential nominee.
Mr Jindal, who was earlier a Congressman, is scheduled to speak on September 3 (between 10 pm and 11 pm local time), which is the prime time. His speech will be followed by the announcement of the party's vice presidential nominee.
Rush Limbaugh, a conservative talk show host, was among the first to propose Mr Jindal's name for vice presidency. Some local and national newspapers have also endorsed him to be on the party ticket.
His youthfulness, conservative Christian values and experience in fiscal matters were cited as reasons in this connection.
The Louisiana governor was the second Congressman of Indian origin, but has become the first Indian-American governor of a US state.
Some speculate that he will be named McCain's deputy on August 29, the 72nd birth anniversary of the GOP's presumptive presidential nominee.
On NBC's Meet the Press programme, Mr Jindal reiterated he had the job he wanted (the Louisiana governorship). ''I am voting for Senator McCain. I will certainly do what I can to help him get elected. I will do it as governor of Louisiana,'' he said, ruling himself out for the vice presidential job.