"His best running mate, by the way, would be Ivanka," Corker told CNN's Manu Raju during an interview on Capitol Hill.
He noted that although he knew this option "would not pass muster," he found the presumptive Republican nominee's daughter "most impressive."
Corker added praise for other members of Trump's family: "As is Eric (Trump), as is Jared (Kushner, Trump's son-in-law and Ivanka's husband). Very close relationships."
Eric Trump also praised Ivanka on Fox News on Thursday.
"She's certainly got my vote. She's got the beautiful looks, she's smart, she's smart, smart, smart," he said, adding that he had "no announcement to make on VP."
The Tennessee senator said that on Tuesday, as he campaigned with Trump in Raleigh, North Carolina, he met with Ivanka Trump and Kushner, who have both played large roles in the campaign.
CNN has reported that Ivanka Trump, 34, has played a pivotal role in convincing her father to fire campaign manager Corey Lewandowski. The businesswoman and mother of three has also been an outspoken surrogate for her father -- and has risen to his defense during moments of controversy.
She has been especially outspoken on his treatment of women, telling CNN's Poppy Harlow in October that she thinks her father would be "amazing" for women.
"I don't think that he's gender-targeted at all, she told Harlow. "I wouldn't be the person I am today, I wouldn't be a high-level executive within his organization, if he felt that way."
Kushner has also played an increasingly large role in the campaign
-- providing assistance with everything from fundraising to speech writing to selecting a vice presidential pick.
Trump said last week that several of his children -- as well as his wife Melania -- will speak at the convention in Cleveland.
But if selected as her father's running mate Ivanka Trump would pass the constitutional age threshold of 35, just barely. Her birthday is in October, less than three months before inauguration.