I would be very surprised if Hamas goes to Turkey. I would also be surprised if they go to Port Sudan.
The problem is that no one wants them and Qatar is now desperately wants to be rid of them.
As some added spice, OPEC+ overestimated Chinese demand and so it it unlikely they will be able to ramp up production to their targets anytime soon. They are also concerned that US tariffs and potential US overproduction could further weaken demand. Combine that with the potential end of the Ukraine war and lessening of Russian oil export restrictions and OPEC+ is concerned about future revenue estimates…
All of this makes the hot potato game with who gets stuck with the Hamas leadership that much more high stakes. Maybe Turkey takes them, but there is little benefit to having them in your country at this point. Is it really worth the headache now since they are already walking the tightrope between NATO, the US, and Russia with Ukraine?
Russia supports a Palestinian state but is staunchly opposed to any form of Islamic terrorism, and are in between on how to treat Hamas as a whole. I am not sure how Hamas being in Turkey works with that whole equation. As much of Erdogan likes to try to ride the line leveraging the tensions between the US and Turkey, and even the Arab nations to a point, this would probably put way too much of a target on Turkey if Iran, via Hamas, does something stupid. Worse, by giving Hamas a home, they are in essence siding with Iran, which has an extremely complicated relationship with Turkey and regardless how it would be framed cause a portion of Turkey be distrustful/upset of the situation.
Could it happen? Sure. I would bet against it at this point though. What is strange is there is no real options for Hamas at all. It is really easy to come up with reasons not to house them anywhere outside of Iran, and I am real short on reasons to take them anywhere else on the Arabian peninsula.