Giggs is said to have been furious at previous reports of a bust-up, but Bosnich believes that the United camp is far from harmonious.
"It has been obvious for some time that things are not quite right there," Bosnich told talkSPORT. "I'm hearing very strong rumours that Ryan Giggs has had a falling out with the management and that is a real shame because that is somebody there with exceptional experience.
"I mentioned those rumours about Giggs and I don't think he is the only one [who is unhappy] so there are a massive amount of problems there and they need to be sorted quickly."
United are currently seventh in the Premier League table, 12 points adrift of a Champions League spot.