@MalinKanji
I was able to place the stairs with no problem pretty much everywhere there was room inside the walls for the footprint. A stair in a room with the low wall requires 5 tiles. On the floor where you place the stairs, it needs 1 for the lower landing and 3 for the stair object itself, plus 1 tile on the floor above for the upper landing. It only takes up 4 tiles on the lower floor though. And if look at a stair from the floor above, the opening a straight stair makes is always 3 tiles, regardless of height (low, medium, tall), so you have to have at least 3 tiles for the stair object on the floor below plus one for the lower landing although the taller walls do require 4 and 5 tiles below if you keep the default stair object base. I usually delete the base so I can use the extra space underneath.
I did try placing the stair pretty much everywhere you can. Against the perimeter walls, middle of the room, in the corners. Worked everywhere as long as there was room for the footprint.
The only thing I can think of that may be affecting you is what is above the floor you show that is not shown in the pic. I tested with nothing above. If you have a room up top that is the same size as the one below, where you show the stairs would conflict with the perimeter wall above as there is no place for the upper landing. I was actually surprised while I was testing when the stairs placed without anything for the upper landing to land on since I didn't make any walls for the upper floor. Sims couldn't use the stair that way though since the upper landing had nothing under it.
One other thought. What is your base? Did you use the wall or room tool to make your room so that it has a foundation? Or did you draw a platform and then put the walls in? Platforms do cause some odd things to happen. And if you made a platform and deleted it and then drew your walls, platforms had an issue that you couldn't place anything else in the tiles where the platform had been. It's been fixed mostly but I still have it happen from time to time in my game. Exiting the lot to the map and returning usually fixes it when it does happen. Sometimes, it requires a save and quit and restart to fix it but one or the other always works for me when it shows up.
Hope this helps.