Well, there are a few moving parts to the answer to your question.
This depends on your situation and that of your training center.
First, let's clear up a little bit of misunderstanding that many people have about DPEs and TCEs:
Under Part 142, you need both a Training Center AND a Training Center Evaluator (TCE) to issue a type rating. A TCE can not issue type ratings absent the authority of the specific Training Center (or centers) for which they have been authorized by the Training Center's POI (Principal Operations Inspector). If I am a TCE for ABC Training Company, I cannot go give checkrides for XZY Training Company without formal written authorization from the FAA.
This is completely different than being a Designated Pilot Examiner (DPE) who can type you in any aircraft for which he is authorized anywhere in the US (as of October 2018). He does not have to work for a training center to complete checkrides. However, in order to use a DPE, you must complete the checkride in the actual aircraft. There are some DPEs that are also TCEs but the authority under which they issue the type rating is based on their authorizations from the FAA. For example, one of our TCEs is also a DPE. The FAA allows him to conduct type rating checks under Part 142 as a TCE but not under Part 61 as a DPE.
Flight training facilities that operate in foreign countries under US FAR Part 142 regulations can (and do) issues type ratings on US certificates all the time. Flight Safety is one of those companies. The have Part 142 approved TCEs on staff to conduct FAA checkrides for those type ratings.
IF (and I say IF) the training center where you train is approved by the FAA to issue type ratings under Part 142 then they could issue you a type rating on both of your certificates upon completion of your training and checking. We do that is the US for various other countries.
If your training center does not have that authority and you still want the type rating on your US FAA certificate, then you have a couple of different option depending on how your US certificate was issued to you. If your US certificate was issued based on your foreign certificate (ie - not a stand-alone FAA certificate), then you can go through the foreign certification verification process, take and pass the Foreign Instrument Written test and then the FAA will issue you a new private pilot certificate based on your foreign certificate with the type rating attached.
If you hold a stand-alone US FAA certificate, and you attend a non-FAA approved training center, there is no way (that I am aware of) to get your foreign type rating added to your stand-alone FAA certificate. You would need to take and complete a US FAA approved Part 142 type rating program or a part 61 in-aircraft program.
Also keep in mind that if you hold a stand-alone FAA certificate, the FAA will allow you to surrender that certificate and to go through the foreign certification verification process (including taking the foreign instrument written) to get a new private pilot certificate based on your foreign certificate with the type rating attached.