Players who decided to leave the PGA Tour and join LIV Golf will not be eligible to compete in next year's Ryder Cup.
Henrik Stenson, who was set to captain Europe in Rome, was stripped of his position after officially joining the Saudi-backed breakaway tour.
Gallacher, who captained Europe in 1991, 1993 and 1995, believes the DP World Tour and PGA Tour will be able to weather the current storm, but will be forced to reach a deal with LIV Golf in the near future.
"If more and more money keeps getting pumped into LIV Golf, then more golfers will join, simple as that," said Gallacher, who is an ambassador for Golf Care. "The traditional Tours won't be able to compete.
"We're in a tricky position now where major champions are switching to LIV Golf and hence potentially not being able to defend their crowns. It's undermining and devaluing golfing competitions on both sides of the Atlantic.
"If things continue as they are, major championships will look completely different in years to come, and we must collectively ask ourselves if that's really what we want.
"A conversation needs to be had and a compromise reached, but I'm not entirely convinced that Greg Norman is the man to have that conversation.
"I think some see him as quite a confrontational character, and you can see why.
"I've known Greg for many years and have played with him several times. He's a very ambitious, savvy businessman but I think he's always had an alternative vision for golf, which has now come to fruition in the form of LIV.
"Greg has a very bullish personality. His whole demeanour doesn't lend itself well to having lots of friends, but we know he doesn't care much about that.
"For me, there needs to be somebody in charge that's amenable to the PGA and European Tours for it to work; Greg Norman isn't that person.
"He's upset the apple cart and ruffled quite a few feathers already and LIV Golf is still in its infancy. It's only going to get worse."