Is it permissible to pay zakaah in advance on every sum of money he saves?

Firstly: 

The way in which zakaah is to be paid on monthly salaries has
been described previously, in the answer to question no.
26113. 

Secondly: 

If a Muslim wants to pay zakaah in advance for every sum of
money he sets aside, there is nothing wrong with that, so long as he owns
the nisaab (minimum threshold), because paying zakaah in advance before
being in possession of the minimum threshold is invalid. 

Ibn Qudaamah (may Allah have mercy on him) said: It is not
permissible to pay zakaah in advance before being in possession of the
minimum threshold, and there is no difference of scholarly opinion on that
as far as we know.  

If he has part of the minimum threshold in his possession and
pays zakaah in advance, or pays zakaah as if he had the minimum threshold,
that is not permissible, because that is hastening to carry out the ruling
before its cause is present. End quote from al-Mughni (2/260). 

It says in al-Fataawa al-Hindiyyah: It is permissible
to pay zakaah after taking possession of the minimum threshold, but it is
not permissible to do so before that. End quote. 

It says in al-Maswoo‘ah al-Fiqhiyyah (23/294): 

The majority of fuqaha’ – including the Hanafis, Shaafa‘is
and Hanbalis, and Abu ‘Ubayd and Ishaaq, are of the view that it is
permissible for the individual to hasten to pay the zakaah of his wealth
before it is due. 

But for that to be permissible, they stipulated that the
nisaab (minimum threshold) must be present; it is not permissible to pay
zakaah in advance before the minimum threshold is there, and there is no
difference of opinion concerning this matter. End quote. 

And Allah knows best.