Jindal, 43, who has already made frequent visits to key primary states in the US and launched a presidential exploratory committee last month, has previously said that he would made his 2016 plans known after the end of Louisiana's legislative session on June 11.
Jindal is "likely to announce his plans to seek the GOP nomination," CNN quoted a person close to Jindal, with knowledge of the announcement.
The Louisiana governor will make his intentions known at an event in New Orleans on June 24, the report said.
In May, Jindal established a federal committee to formally evaluate a presidential bid and created a web site touting his possible entry into the race.
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"If I run, my candidacy will be based on the idea that the American people are ready to try a dramatically different direction," he said at the time. "Not a course correction, but a dramatically different path."
"My parents came to this country over 40 years ago with nothing but the belief that America is the land of freedom and opportunity. They were right," Jindal said on his website announcing the formation of the Bobby Jindal Exploratory Committee.
Jindal, a former congressman who started his career in public service as Louisiana's health secretary, also tried to strike a difference between himself and other Republican leaders by describing policy plans he has released on health care, defence, energy and education.
Jindal is the 55th and current governor of Louisiana and the vice chairman of the Republican Governors Association.
Meanwhile, a CNN/ORC International survey released yesterday shows that Jindal is polling at 1 per cent nationally.