Following up with Alum... Needs Advice

Hi all, so I saw a job posting that I am really interested in a week ago, and I reached out for an alum on Linkedin for a little chat. He was nice enough to give me his e-mail and ask me to send him my resume. A week has passed and I have heard nothing - either he did not get my e-mail, or my resume is just uninteresting to him. Meanwhile I got a job offer from a fund in HK, but I am not a very big fan of HK... So I wonder: 1. Since the alum did not promise anything (I just sent my resume to his e-mail and that's pretty much it), is it appropriate to ask him for an update, given that I do need to make a decision in two weeks?
2. What is a polite way of asking without sounding too pushy?

Thx!