I don't want to alarm you, but

I don't want to alarm you, but

A phrase used before sharing bad news (which is stated after "but"). I don't want to alarm you, but the printer called about a few problems with our latest issue. I don't want to alarm you, but the dog has been limping around all day—I think we need to take him to the vet tonight.
See also: alarm, but, want
Farlex Dictionary of Idioms.

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
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs.
See also:
  • upset
  • raise the alarm
  • sound the alarm
  • frighten the pants off (of) (one)
  • five
  • fume at
  • fume at (someone)
  • annoy
  • dash out
  • dash away