In his maiden foreign policy speech, Jindal spent a good time chastising US President Barack Obama over his decisions refusing ground troops in Iran and Syria.
"The people in this country are hungry for a big change. There's a lot of frustration," the 43-year-old Republican governor said at the American Enterprise Institute (AEI).
"They're frustrated with the president, but they have yet to hear a comprehensive alternative from the Republicans.
Jindal said he has been "thinking and praying" about a possible run and suggested a decision may come after the November 4 mid-term election or "sometime after the holiday."
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But with some potential competitors deferring until Spring 2015, Jindal could be one of the first Republicans out of the gate.
The two-term governor appeared to be trying to appeal to right-leaning conservatives in his party with an aggressive stance on foreign policy.
He argued for more robust defence spending -- not exactly the usual province of an outgoing governor.
"Within the arena of national defence, the need now is for more funding, not less," he said.
"We must undo the president's harmful spending cuts, and ensure that our fighting men and women always have the tools they need to succeed."
He asserted that a nuclear-armed Iran is not only an existential threat to Israel and other American allies in the region, but a threat to the US as well.
According to early polls, Jindal sits well behind other potential Republican contenders such as Kentucky Senator Rand Paul and Texas Senator Ted Cruz.