The breakaway circuit launched in June and counts 12 major champions among its players but the PGA Tour, in a bid to curb the threat, has made sweeping changes including increased purses and an earnings assurance program.
Players who joined the LIV series are no longer eligible to participate in PGA Tour events.
"The PGA Tour, for the last 20 or 30 years have had all the best players in the world. That will never be the case again. LIV Golf is here to stay," Mickelson told reporters after carding two-under 70 in the opening round of the LIV event in Chicago on Friday.
"The best solution is for us to come together. I think that the world of professional golf has a need for the old historical 'history of the game' product that the PGA Tour provides. I think that LIV provides a really cool, updated feel that is attracting a lot younger crowds...
"Both are good for the game of golf and the inclusion of LIV Golf in the ecosystem of the golf world is necessary. As soon as that happens, we all start working together. It's going to be a really positive thing for everyone," the 52-year-old American added.
American twice major champion Dustin Johnson (38) took a three-shot lead in the opening round after carding 63 to finish on nine-under at Rich Harvest Farms.
World number three Cameron Smith (29) of Australia was second at six-under and Matthew Wolff a shot back in third.
