Yahoo said financial advisers Jason Jernigan and Brahmbhatt declined comment.
The transactions could violate NCAA rules prohibiting benefits from agents or representatives.
Southern California received heavy sanctions for improper benefits to Heisman Trophy-winning tailback Reggie Bush, including a two-year bowl ban, four years of probation, 30 lost scholarships and 14 vacated victories.
Couch is a senior for the Volunteers. Fluker, Bray and Cox are currently playing in the NFL while Bumphis was recently released by the Miami Dolphins.
Alabama athletic director Bill Battle said in a statement that the university was aware of the Yahoo's report.
"We have been aware of some of the allegations in today's story and our compliance department was looking into this situation prior to being notified that this story was actually going to be published," Battle said. "Our review is ongoing. We diligently educate our student-athletes on maintaining compliance with NCAA rules, and will continue to do so."
Crimson Tide linebacker C.J. Mosley said after Wednesday's practice that if the allegations did occur, nothing like that is happening now.
"It was upsetting to hear, but at the end of the day, that's what happened in the past," he said. "The coaches do a great job of informing us and our parents about agents and things like that. So I'm pretty sure that won't be happening again."
Alabama coach Nick Saban said he was confident the university will "handle the situation appropriately."
Saban, who is preparing his top-ranked Tide for Saturday's visit to No. 6 Texas A&M, said he hadn't read the report, but praised how Alabama players have avoided temptations.
"For as many high-profile players as we've had around here, I'm fairly pleased with the way most of them, for the most part, have managed their circumstances and their situation and focused on what they need to do for the University of Alabama," he said.