I interviewed for two different companies, one of them offered me a job, but the other one is still in the process, I know they liked me and I liked them very much, however, I do not know if it is appropriate to mention that I received an offer. I do not want to sound pushy. But I only have days to accept the offer from the other company. So I am not sure what to do. Any advice will be helpful. Thanks.
Hiring managers aren't going to be shocked that candidates are interviewing elsewhere and might be getting other offers. It isn't surprising, therefore, when candidates contact a hiring manager saying something along the lines of
"I appreciated speaking with you and I'm really excited about the opportunity. I wanted to let you know that another company has given me an offer that I need to decide on by <>. If there is anything you can do to expedite your decision, that would be very helpful."
That's not pushy, just professional-- you're letting them know that something has changed since you last spoke. Sometimes they'll be able to get you an offer quickly, sometimes they won't be able to get you an offer before your deadline and you'll have to decide whether to accept the offer in front of you or hold out hoping for a better offer from someone else.