Ekpre-Olomu was recently cut by the Cleveland Browns, who drafted him in the seventh round last year.
Miami lacks cornerback depth and was ranked 21st in pass defense last season. The team released Pro Bowl cornerback Brent Grimes and acquired Byron Maxwell in a trade with the Philadelphia Eagles. But the No. 2 cornerback and nickel roles are wide open for the Dolphins, who will begin their offseason program on April 11.
Ekpre-Olomu is currently recovering from a serious knee injury that forced him to miss the entire 2015 season. In February, he said in an Instagram post that "I'm not quite 100 percent yet, but I'm close."
The 5-foot-9, 195-pounder was projected to be a first-round pick before he injured his knee as the Ducks prepared to play in the national championship against Ohio State.
Ekpre-Olomu started 40 straight games in college before getting hurt.
The Associated Press contributed to this report.