"I do think, he (Jindal) will run... He would be a significant candidate," Senator David Vitter told American TV channel C-SPAN's Newsmakers programme.
"I like Bobby, I respect his leadership, I agree with all of his political values. But I haven't thought about what I would do or wouldn't do personally," Vitter, also a member of Republican party, said.
"Oh yeah. I think that's very obvious to everybody who has been paying attention," the Senator said when asked if he believes Jindal, 42, would to be the next president.
Jindal's second term as the Lousiana Governor ends in 2015. He can't run for the third term. Vitter is considering running for governor.
Jindal had earlier did not rule himself out from entering the presidential race in 2016, but said, "I think it's too early."
"I would expect we will come to a conclusion sometime in January," Vitter said.