Following the news, Pietersen, who was axed by England after their Ashes defeat to Australia last winter, wrote on Twitter: "Where do I apply for ENG batting coach job? I promise I won't encourage whistling when you get out or trying to change the game!"
When asked by Sky Sports News if Pietersen is speaking too much, Cook said: "Some people like to do their business on social media and others don't.
"Obviously a lot has been happening over the last few months on that front with KP and that is what it is. We as an England side have moved on and we'll move on without him over the next few years."
Cook also claimed that he does not expect his captaincy role to change under Moores's leadership.