The person didn't want to be identified because the Dolphins and Cowboys hadn't confirmed the trade. The Dolphins have repeatedly tapped the Dallas pipeline since the arrival of former Cowboys coach Bill Parcells in December to run Miami's football operations.
The draft pick is No. 100 overall Saturday. The Dolphins have eight other picks and will use the No. 1 overall choice to take tackle Jake Long, who has already signed a five-year contract worth $57.75 million, $30 million of it guaranteed.
Ayodele has been a starter for the past five seasons and made 55 tackles last year. His spot with the Cowboys may be filled by Zach Thomas, acquired after the Dolphins released him in February.
Fasano, a second-round pick in 2006, has made 14 receptions in each of his first two NFL seasons and is expected to contend for a starting job with the Dolphins.
Miami will still be looking to upgrade in the draft at quarterback, cornerback, defensive end, guard and receiver.