The Diamond League meeting in Eugene, Oregon, would have been the first race of the 25-year-old's career in the United States and was expected to be a preview of the 110 metres hurdles final at the London Olympics.
The delay in obtaining a visa for Robles and his Cuban team mates, however, was likely to scupper world record holder's participation, his coach said.
"It is unlikely that we can compete in Eugene," Santiago Antunez said.
"Everything is delayed and then he would have to race the top eight (hurdlers) in the world."
Robles had hoped to fly to Oregon on Wednesday so he could be well rested for Saturday's clash but the visas, while approved, will not be ready for collection until Thursday, Antunez said.
That made Antunez cautious about sending Robles out at less than full strength against a field that would include the three fastest high hurdlers of all time.
Resurgent 2004 Olympic champion Liu Xiang, who posted the best time of the year in 12.97 seconds earlier this month, and U.S. record holder David Oliver are also set to line up for the race.
World champion Jason Richardson, who was handed the gold in Daegu last year after Robles was disqualified for impeding Liu in the final, and indoor world champion Aries Merritt, both Americans, will also run.
"This competition is an Olympic final," Antunez said.
Prefontaine Classic organiser Tom Jordan said he had heard nothing official from the Cubans.
"Until I do, I cannot comment," he said.
Robles also wants to compete in the New York Grand Prix on June 9.