Speaking to reporters ahead of the start of his Hero World Challenge event in New Providence, Bahamas, Woods said Norman “has to go.”
Asked if the LIV Golf series and PGA Tour can co-exist, Woods said: “Not right now, not with their leadership, not with Greg there and his animosity towards the Tour itself. I don’t see that happening.”
Following the launch of the LIV Golf series earlier this year, the sport of golf has been divided with many of the top players from the PGA Tour moving to the rival series.
Earlier this year, LIV Golf joined an antitrust lawsuit alongside some of its players, alleging that the PGA Tour threatened to place lifetime bans on players who participate in the LIV Golf series.
The suit also alleges that the PGA Tour has threatened sponsors, vendors and agents to coerce players to abandon opportunities to play in LIV Golf events and access to their members.
The PGA Tour filed a countersuit in late September, claiming “tortious interference with the Tour’s contracts with its members.”
The LIV Golf series is backed by Saudi Arabia’s Public Investment Fund (PIF) – a sovereign wealth fund chaired by Mohammed bin Salman, the crown prince of Saudi Arabia.
In the inaugural season of the controversial, big-money tour, former world No. 1 Dustin Johnson won the individual championship title and $18 million in prize money.
Woods – who returned to golf earlier this year following serious injuries sustained in a car accident – has previously voiced opposition to the LIV Golf series, and on Wednesday, he reaffirmed his stance.
“I think Greg has to go, first of all, and then, obviously, the litigation against us and then our countersuit against them, those would then have to be at a stay as well,” said the 15-time major champion. “Then we can talk, we can all talk freely.”
In an interview with Fox News aired in August, Norman said Woods turned down an offer worth approximately $700-$800 million to join the LIV Golf series.
Earlier this month, world No. 1 Rory McIlroy also called for Norman to stand down from his position at the top of the breakaway series.
LIV Golf declined to comment on Woods’ latest remarks when contacted by CNN.
Woods has not competed since July and announced this week that he was withdrawing from the Hero World Challenge with plantar fasciitis – pain in the base of the foot.
“It was a tough decision just because I want to play,” Woods said. “I like playing, I like competing, but unfortunately – I can hit the golf ball and hit whatever shot you want – I just can’t walk.
“I’ve had a few setbacks during the year that I still was able to somehow play through, but this one I just can’t.”
He said his goal next year is to just play the major championships and one or two other tournaments as that’s all he can handle physically.
CNN’s Kevin Dotson contributed to reporting.