Will Air New Zealand go for A350-900 and 777-8/9x order?

Air New Zealand needs to upgrade their 772 fleet what will they do? Will they go for A350-900 or 777-8x 

Seriously, this is a bit of a silly question. Unless anybody here is from Air New Zealand and cares to answer your question, all you'll get is ambit speculation which has little if any currency. That said, given that Air New Zealand flies an all-Boeing international fleet in the 777 and 787-9, it's only commonsense to expect they would go for a Boeing.

The oldest 777 in Air NZ's fleet is 12 years old. Incremental aircraft (if any) will be more 787s, while replacement of anything is a good 8-10+ years away.

They have 2 767s left.  It would be likely they will replace those with 787-9s soon. 

Air NZ still has 3 789's on order with options for additional 6. There are no plans at this stage to purchase any new Boeing aircraft. The replacement review for the 772's in not due until late 2018 or 2019.

I suspect Boeing must have inside running given desire ANZ has rightly shown to reduce fleet types / variants.

I don't know what they'll do. However, I think it is quite possible Air New Zealand will go for the A350.

AIr NZ is going to lease another B789 from 2019 making the B789 fleet to 13 aircraft. I suspect that Air NZ with 5 options still available, with make the B787's as their main fleet for international medium to long hauls routes backed up with B773's.

There is word that Air NZ, being the launch customer for the B789, is working with Boeing for a possible B787-9ER version to compete with the A350-900LR. Also Boeing is is pushing hard for Air NZ to use the B787-10.