Z.B.: Can we talk / may I call you (still) today?

I would actually leave out "still" as "still today" sounds strange here - but don't worry, the sentence with it would probably be understood.

If it's important to emphasize that you'd like to talk/call before tomorrow, I would suggest either indicating approximately the time you're thinking of ("this afternoon," "this evening," or whatever) or:

"Can we talk/Can I call you before the day is out?"

But generally, today is today, and that's all you need.

In case you're wondering: "Can we still talk today?" would indicate that the plan to talk today had already been agreed on, and you're wondering whether that plan has (or has to be) changed.

I agree, Janette. I was thinking I ought to write a comment -- now I don't need to!

Oder so: "Can I please call you? - Today?" (non-native suggestion)

Hi Janette B.!

Can I talk to you today before you leave the office?

I missed this yesterday - yes, Tho_991, that's a great formulation. (Or was it a serious question? My PMs are open...) :-)

Diesen Unterschied sehe ich auch, Tho.