If this is an air source heat pump--most likely as they are the most common--it may not be advisable to enclose it as it uses the air as a heat source or sink. Check the manual, manufacturer's website or technical line or your supplier before enclosing it.

Thanks worthy, I'll double check..it is a hp. I did ask the salesman who sold it to me who said it could be enclosed and in fact said he'd come back and put a return thru my wall into the unit when I 'finished' my basement...that was year ago!

Still I'll double check. Would drywall be necesary both inside and out?

Enclosure is probably not the best description. You can surround it as long as you leave sufficient room for ventilation. See, for instance, the answer by this energy supplier.

Drywall around any return would look more finished. Certainly, drywall isn't suitable for exterior use.

I think I confused you. I am talking about the part of the heat pump that resides in the house...in the basement.

Oh well. It can't hurt to post a hopefully helpful answer to a question that wasn't asked.

For operation, enclosing the unit is no problem providing you provide a louvered door or dedicated return air ducting so the air can get into the unit, however you MUST make sure that you leave sufficient access for maintenance, including removing the fan/motor assembly.