Well after further research, the answer is: No, it’s not possible right now to get a mobile device id number from its browser…
A solution I found is to generate a “unique” number (in my case I worked with php, so I used the session_id() number mixed with a number generated with the rand() function, it ends up being a quite big number that will hardly occur twice…) and then store it in a cookie that never expires.
It’s not a perfect solution, as it will not work if cookies are disabled or if the user clears his cookies, but actually after using it for sometimes now, it turns out that it is working quite well, mobile device mostly have cookies enabled, and the users don’t seem to clear them often…
Also (depending of your application) if you store an email or a username and then associate it with this “unique” number into a database, you can even recover someone’s identity and store a new cookie by asking him his username or email again…
Hope this will help some people!