So according to Mr. Demir, he mentions "one or two (different) readily available engines to be used for the interim", before the Turkish developed engine is ready. This to me sounds like he's talking about an engine other than the F110.
Now considering what we have heard so far from various official Turkish figures, it seems to me that this "1 of the or maybe 2 of the engines" that he is talking about is firstly the F110, which has been licensed to Turkey for local production of parts and assembly for F-16 and another engine from a different country, probably Russia. I guess they are planning to use the F110 for the prototype and are going to apply for the US approval of using those F110s for what they are intending, which is not the application on F-16.
If the US doesn't approve, they could go ask this unknown second party, once again probably Russia, for an engine. In case if its really Russia, they seem to be willing to sell Su-35s and Su-57s, so maybe they are also willing to sell their engines if not the jets.