I don't want to alarm you, but

I don't want to alarm you, but

 and I don't want to upset you, but
an expression used to introduce bad or shocking news or gossip. Bill: I don't want to alarm you, but I see someone prowling around your car. Mary: Oh, goodness! I'll call the police! Bob: I don't want to upset you, but I have some bad news. Tom: Let me have it.
See also: alarm, but, want