H1B Transfer When Passport is about to expire

Dear Members,

I am currently working with employer A in US on H1B visa. Now, I have an offer with employer B, but my passport is expiring on April 2016. Would it cause any problem if I transfer H1B visa to employer B when my passport is about to expire?

Or is it a good idea to renew the passport and then transfer the visa?

Any adivce in this would be immensely appreciated. Thanks.

Your passport expiration or renewal will not impact the H-1 cap-exempt petition that will be filed by B.