Student or Learner
I want to talk to Jane over the phone.
"Could you please put me through to Jane" or "through to the department in which Jane works".
"Could you please put Jane on line".
I'm not a teacher. I speak American English. I've tutored writing at the University of Southern Maine and have done a good deal of copy editing and writing, occasionally for publication.
Also, if you are going to ask to be put through to a department, it would be better to give the name of the department.
tufguy, you might try saying Could you call Jane to the phone, please? or Could you put Jane on the phone, please?
I find neither of those very natural.
See post #2.