The former Wales and Liverpool forward currently works for Cardiff City as their player development manager.
According to The Telegraph, Bellamy has been selected by the U's board after a thorough recruitment search over the past few weeks.
"We want to facilitate Craig's opportunities to get experience," Cardiff chief executive Ken Choo is quoted by the newspaper as saying. "This could be a good move for his career."
The 38-year-old was interviewed for the Wales job before his ex-teammate Ryan Giggs was appointed in January.