Is there anything on door frame like draught excluder?

In the UK this is often foam or short bristle but can be "P" shaped rubber strips. It could be this that's sticking to the door, particularly if it's old and has got dirty.

If you remove this does the noise go away.

Another possibility is the hinge, but the noise you describe doesn't sound like the sort of noise a hinge would make. A short squirt with WD40 or light oil will lubricate the hinge - something you might want to do anyway.

Is there anything on door frame like draught excluder?

In the UK this is often foam or short bristle but can be "P" shaped rubber strips. It could be this that's sticking to the door, particularly if it's old and has got dirty.

If you remove this does the noise go away.

Another possibility is the hinge, but the noise you describe doesn't sound like the sort of noise a hinge would make. A drop or two of light oil will lubricate the hinge - something you might want to do anyway.