New England Patriots owner Robert Kraft did little to clear up the mystery of how Russian President Vladimir Putin ended up with his Super Bowl XXXIX ring.

But on CNBC Wednesday, Kraft made Putin an offer: "The [Russian] president has made a comment that he's making me a new ring. So we want to invite him to come here and give it to us on NBC, during one of our national games here."

Kraft's overture came during an appearance on "Squawk Box," promoting this week's start of the NFL's regular season.

While visiting Russia in 2005, Kraft said then that Putin admired the ring and took it without permission—a claim he later retracted, saying he gave it to Putin as a gift.

Kraft told CNBC Wednesday: "I gave it to him as a gesture of friendship. And this thing developed into a bigger story. We're having fun with it."

—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.

