Coulter -- a wide receiver out of Rhode Island who the Texans' selected with the 171st overall pick in the fifth round of the NFL Draft on Saturday -- played for Jim Fleming in college.
Fleming was the defensive coordinator at Brown University in 1993 -- five years before Coulter was born -- when Bill O'Brien got his start in coaching as Brown's tight ends coach.
Harris said from a wide receiver standpoint, the Texans get good value with Coulter in the fifth round.
Coulter met with the Texans at the NFL Scouting Combine and via FaceTime leading up to the draft. He called it "a great fit" and said he's eager to contribute on special teams as well as at wide receiver.
At Rhode Island, Coulter mainly played outside receiver.
"But I feel like I can play anywhere if given the opportunity.," he said.
"I play with a chip on my shoulder," Coulter said. "I just want to help out any way I can. I know I come from a smaller school ... but once you get on this level, you have to prove yourself. So I'm just trying to prove myself."