No, you can only take it for the first square
I can see how this would be beneficial, and as a DM I would probably rule you could however by RAW you cannot. The important rules are found under Making an Attack of Opportunity (emphasis mine):
An attack of opportunity is a single melee attack, and most characters can only make one per round. You don't have to make an attack of opportunity if you don't want to. [...]
An attack of opportunity "interrupts" the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue [...]
When the target triggers the attack of opportunity with their first square of movement you immediately decide if you want to take the attack or not. You then immediately resolve it.
There is some ambiguity that if you choose not to take it you could take it as they trigger from further movement. However this is covered by the rule under Additional Attacks of Opportunity:
Moving out of more than one square threatened by the same opponent in the same round doesn't count as more than one opportunity for that opponent.
So no, you either take it in the first triggering square or not at all.