What is the correct phrase to use?
I am speaking on the phone? Please keep quiet for a while.
or
I am talking on the phone? Please keep quiet for a while.
To me, the first one makes more sense.
Both are perfectly grammatically correct.
Also, to me, it sounds more natural to say "I am speaking with someone on the phone", rather than simply just "I am speaking on the phone". But perhaps that is just my personal preference.