If at least half of the final round is completed Monday before more expected rain arrives then the remaining holes will be pushed to Tuesday.
"We will do everything we can to play tomorrow and we will see what Mother Nature gives us (Monday) morning", White said.
PGA Tour policy states every feasible attempt must be made to complete 72 holes, but also that a final round can not begin on a Tuesday.
Final-round results will decide the 30 players who qualify for the season-ending Tour Championship in two weeks at Atlanta.
The 41-year-old, who is looking forward to playing in the Ryder Cup for the first time since 2008, won his first PGA Tour title for nine years at the Valspar Championship in March, when he held off Tiger Woods and Patrick Reed to clinch a one-shot victory.More news: Florence expected to become 'major hurricane' Monday
More news: IPhone XC: The colorful budget-friendly Apple phone
More news: US Open champion Osaka storms into the top 10
It would clearly be a huge boost for Europe's Ryder Cup hopes if Rose was successful and, indeed, if he proceeded to win the $10million (£7.7million) FedEx Cup bonus at the Tour Championship on the Sunday immediately preceding the biennial dust-up.
Finally, Bill Haas, who has played a part in three winning Presidents Cup teams, might have been a decent shout for a Ryder Cup spot not too long ago but the 36-year-old has missed 10 cuts in 22 starts in 2018, leaving Furyk with a hard choice between Schauffele and Finau on Monday.
The pick was to be announced a short time after the BMW Championship ends, whenever it ends. He needed 30 putts on Saturday. Spieth also must qualify for the season finale to play the minimum 25 events this season or face a fine.
"Nor would we start a round on Monday thinking we could not get half the field finished", he said.
He has shot 61 four times on the PGA Tour, most recently at the 2013 Bridgestone Invitational. For someone like Bradley, getting to the Tour Championship would get him into all four majors next year.