A host of top players have joined the breakaway tour, which Woods said at last month's Open he disagreed with.
In an interview with Fox News' Tucker Carlson, Norman confirmed the 15-time major champion was offered about £575m to £650m to join LIV.
"That number was out there before I became CEO," said Norman.
"Tiger is a needle-mover, right? So of course you're got to look at the best of the best. That number is somewhere in that neighbourhood.
"They had originally approached Tiger before I became CEO."