USA Track & Field spokeswoman Jill Geer has said the re-run between Allyson Felix and Jeneba Tarmoh needs to take place by Sunday to allow the governing body time to finalise its team.
She said on Wednesday if there was to be a run-off the governing body would announce its plans on Saturday or Sunday.
Kersee, whose athletes will be competing in the women's 200 beginning on Thursday with the final on Saturday, said he would be upset if any race between the two took place before Tuesday out of concern for the athletes' health.
"To force their hands to run on Sunday, that's detrimental to the athletes," the respected coach told Reuters.
"The body needs a normal rest. It is hard enough to run three days in a row as is."
Tuesday is the last day for USATF to submit team members to the U.S. Olympic Committee for approval, committee spokesman Mark Jones said.
The team must be forwarded to Olympic officials by July 9, he said.
Twice Olympic 200m silver medallist Felix and the up-and-coming Tarmoh have a choice of a run-off or coin flip if one of them does not withdraw, according to a USATF procedure announced on Sunday.
The governing body had no protocol in place for ties at the Olympic trials before then.
Only three athletes per country can qualify in the 100m sprint at the Olympics.
"I am trying to stay neutral," added Kersee. "But I can't stay neutral when it comes down to the health of athletes."
The coach said he had no preference on a location if a run-off is held.
"I just care about what day they have it," he said.