Shonn Greene (born August 21, 1985) is an American football running back who is currently a free agent. He played college football for the University of Iowa, and was recognized as a unanimous All-American.He was drafted by the New York Jets in the third round of the 2009 NFL Draft.Greene has also played for the Tennessee Titans.e played college football for the University of Iowa, and was recognized as a unanimous All-American. He was drafted by the New York Jets in the third round of the 2009 NFL Draft. Greene has also played for the Tennessee Titans.