I know Azan is the best time to ask for a Dua. But whatever you think during does it become real? I mean you are not making a Dua it's just an imagination.
This belief has no basis in Islam and hence cannot be considered as true. Definitely when Allah wills things happen however, Allah has clearly mentioned throughout the Quran his sunnat (practice) when it comes to accepting dua etc.
Allah says in Quran in 2:186
And if My servants ask you about Me, I am near answering the calls of those who call to Me. So let them respond to Me and believe in Me that they may be guided.
So, Firstly this has not much to do with Azan. Secondly, the act of dua is the belief that Allah can make happen what you wish for and so you ask him for it.
Thinking of something during Azan is not dua nor is about asking Allah for something. So this belief has no basis in Quran or Islam