Five of the 54-hole tournaments have already been held this year, for which a number of top names signed up, with the final three scheduled for Bangkok, Jeddah and Miami.
However, an application made in July for the LIV series to be awarded world ranking points - the metric by which most players qualify for majors, World Golf Championship and other top events - remains undecided.
As a result the 48 players who featured in last week's tournament in Chicago, including Open champion Cameron Smith, six-time major winner Phil Mickelson and the likes of Brooks Koepka and Bryson DeChambeau, have written to OWGR chairman Peter Dawson, former chief executive of the R&A, asking for a resolution.
"As the athletes who are ranked, we depend on OWGR not just to qualify for the most important events, including the majors and Olympics, but to tell us where we stand among our peers," said the letter.
"To maintain trust, we urge you - as one of the true statesmen of sports - to act appropriately to include, on a retroactive basis, the results of LIV Golf events in OWGR's ranking calculations.
"An OWGR without LIV would be incomplete and inaccurate, the equivalent of… leaving Belgium, Argentina, and England out of the FIFA rankings.
"Every week that passes without the inclusion of LIV athletes undermines the historical value of OWGR.
"We call on you to render a positive decision quickly - for the benefit of the integrity of the rankings, the game and all of us who love the sport."
The established tours' response to the LIV threat has varied with the PGA Tour immediately suspending players the moment they teed off in the breakaway. The DP World Tour has encountered difficulties with a similar decision challenged in the courts which resulted in a stay on disciplinary action.
Legal challenges are pending on both sides of the Atlantic but the non-allocation of ranking points to LIV means the two main tours can still operate from a position of relative strength.
However, it has been suggested the delay in any decision from the OWGR - which has a governing board which also comprises top executives from both main tours, the R&A, the PGA of America, USGA and Augusta National Golf Club, further strengthens their hand.
"As time goes by, LIV golfers automatically decline in the rankings," added the players' letter.
"We hope the story we read today about the decision being slow walked so LIV golfers will slide down and to harm LIV is not accurate.
"For example, Dustin Johnson was ranked 13th on OWGR shortly before he announced he would play in LIV tournaments. He now ranks 22nd - despite finishing eighth, third, second, and first in the first four LIV events."