updated 3:58 p.m. ET Sept. 1, 2009

COLUMBUS, Ohio - Former Ohio State running back Archie Griffin, the only two-time winner of the Heisman Trophy, says he’d welcome being joined in that elite company by Florida’s Tim Tebow or Oklahoma’s Sam Bradford.

“I’ve always said that there’ll be somebody else who wins it twice,” Griffin said Tuesday. “It would not be a surprise to me if someone were to do it this year.”

Tebow won the award two years ago as a sophomore and is quarterbacking the nation’s No. 1-ranked team. Bradford, who won the Heisman last December as a sophomore, returned as quarterback for the Sooners, who are ranked No. 3.

Asked if it would be difficult for his ego to no longer be the only two-time winner, Griffin laughed.

“One of the things that I can always say, I was the first,” he said. “That will always be. So if there’s anything that I need to brag about, I guess I could always brag about that. But it’s not a thing about bragging, it’s a thing about judging talent and giving people an award that they deserve. And if someone is deserving of the award I will not hesitate to vote for them even though they have won one Heisman Trophy.”

Griffin won the Heisman in 1974 and 1975. He is president and CEO of Ohio State’s alumni association.

Bradford said he admired what Griffin went through to win the award twice.

“That’s a tremendous accomplishment. Just to win one is extremely challenging and to win two is really hard to describe,” he said. “Obviously if the award’s been given out for 70-plus years now and nobody’s ever won it twice except for him, it’s an extremely difficult task.”

Griffin said one of the challenges in trying to win the award a second time is dealing with demands on your time.

“Everybody wants a piece of you. You have to make sure that you’re not distracted so much that you don’t pay attention to what you should be doing out on the football field,” he said.

Griffin said that his coach at the time, Woody Hayes, called him into his office and told him he was trying to please too many people by making appearances and going to banquets.

“Coach Hayes told me that you can’t do everything for everybody,” he said. “He said, ’You keep doing all of this and it’s going to make you soft.’ So one thing I had to make sure I did was to be the best football player that I was going to be. That meant taking care of the things that I had control of — how I prepared for the season.”

Bradford said he felt he and Tebow are approaching the season in the right way.

“As far as me and Tim going after a second one, I think either of us, that’s the last thing on our mind right,” he said. “I’m not sure who they (the Gators) open up with, but we play BYU Saturday and that’s all I’m concerned with right now.”

Griffin, who rushed for 5,589 yards in his college career while stacking up an NCAA-record 31 consecutive games with at least 100 yards rushing, votes for the award each year. He said he considers statistics from the current season, past performance, victories — and character.

He said the top finishers a year ago — Bradford, Tebow and quarterback Colt McCoy of Texas — are exemplary people.

Special feature Heisman Hopefuls Who will win prize this season? NBCSports.com

All are back for the upcoming season. Tebow and Florida play Charleston Southern and McCoy, a senior, leads the No. 2 Longhorns against Louisiana-Monroe.

“I thought the top three were terrific,” he said of the leaders in the Heisman balloting. “I actually thought the vote would be closer than it was. Any of those three guys deserved the Heisman Trophy. I felt good about any of those three guys winning. Their character is outstanding and when you read about all the things that they’re doing, it’s amazing. I just hope they continue to do those type of things, because they are impacting people on their campuses and certainly in the communities in which they live. They’re great role models.”

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