The former United shot-stopper believes there are a number of problems behind the scenes at the Theatre of Dreams.
Manchester United have had a nightmare campaign under new management and currently sit in seventh place in the Premier League table.
The Red Devils hit rock bottom as they were humiliated 3-0 by Manchester City on Tuesday night and now Bosnich has insisted that there are problems between Moyes and Giggs, who is on the coaching and playing staff at Old Trafford.
Bosnich told Alan Brazil Sports Breakfast: "It has been obvious for some time that things are not quite right there.
"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.
"There are things seeping out that things are not well behind the scenes. The fact that a lot of old players are coming out [blaming Moyes], like Paul Scholes, tells me there are definitely problems behind the scenes."
However, Bosnich has suggested that the Manchester United board must back Moyes, but the problems at the club must be addressed sooner rather than later.
Bosnich continued by saying: "The board have to back the manager while he is employed by the club, but they must be concerned behind the scenes with how things are going.
"I mentioned those rumours about Giggs and I don't think he is the only one, so there are massive amount of problems there and they need to be sorted quickly."
Moyes' immediate attention will turn to his side's clash with Aston Villa this weekend. The Red Devils will be hoping to secure all three points against Paul Lambert's side as they look to build some momentum ahead of their Champions League quarter-final clash with Bayern Munich next week.