Jindal maintained that he was satisfied in his current role, but he didn't altogether reject the idea of accepting an offer to be presumptive GOP presidential nominee Mitt Romney's running mate.
"Look, I've got the job that I want. We just passed the most comprehensive education reforms in Louisiana's history. Now we're in the middle of a legislative session ... so I've got the job that I want," Jindal said on CNN"s "Starting Point."
"As symbols go, Louisiana Gov. Bobby Jindal is a doozy: a brilliant policy mind with an inspirational life story who has run an effective government in corruption-tainted Louisiana. He can talk data with Romney and credibly sit at the kitchen tables of the struggling middle class. Which leads to this thought: Bobby Jindal for vice president!," wrote Frum in a CNN column.
Jindal was making the media rounds ahead of a speech at the American Federation for Children National Policy Summit and promoting reforms in his state, but he couldn't escape the political spotlight.
He was also pressed by MSNBC's Chuck Todd on "The Daily Rundown" about his feelings about a potential vice presidential slot and gave an nearly identical answer..
The Louisiana governor told both CNN and MSNBC that he would support Romney regardless of his choice for running mate.
"I don't think it's going to be me. He's got plenty of great, great candidates he can select from, and I'm going to be happy to support the ticket from right here in Louisiana," he said.
Jindal initially endorsed Texas Gov. Rick Perry in the GOP primary race, but Jindal threw his support behind Romney in April following Rick Santorum's withdrawal from the race.