Are you just testing your blood glucose once a day, in the mornings?
Ideally, to spot any high readings you could test before eating and then 2 hours afterwards. That will show if your blood glucose is high after meals.
Just testing in the mornings before breakfast will tell you if you are high then, but it won't tell you about the rest of the day.
The reason we get thirsty with diabetes is usually because our glucose goes so high that it triggers a response from the kidneys. They try to remove the excess glucose by removing it via the urine, and in order to do so, they take fluid from the blood. This makes us thirsty in order to replenish the liquid.
This mechanism is usually triggered at around the 10-11mmol/l blood glucose level, although it varies a little between individuals.
So if you are getting a diabetes thirst, I would suggest that your meals may be spiking you higher than you think.
On the other hand, if your blood glucose stays low, and you are not spiking to 10 or above, then your thirst may be being caused by something else. Food seasonings? Hot weather? Exercise? Monosodium glutamate always makes me insanely thirsty, and sometimes I haven't got a clue I have eaten any, until the thirst strikes.
I would suggest doing some testing around meals, which will inform your next step - adjust diet, or go see your doc for further investigation.
Hope this helps.