Woods injured his back midway through the final round at the WGC-Bridgestone Invitiational on Sunday - in just his third competition since returning from surgery.
The 14-time major winner underwent an operation on his back earlier this year and, after his latest setback, is a doubt for the final major of the year as well as the Ryder Cup in September.
Woods has yet to announce whether he will feature in Kentucky this week, but officials have confirmed he will be given as much time as possible to decide.
PGA chiefs also revealed on Wednesday there had been regular contact with Woods' camp and that an official decision had not been made.
"He has until his tee time to arrive," said Kerry Haigh, chief championships officer for the PGA.
Woods is due to tee off alongside Padraig Harrington and Phil Mickelson at 08.35 local time (12.35 GMT).