Pietersen was dropped for England's last Test against South Africa over a text message dispute and he has been omitted from the squad for November's tour of India.
Speaking for the first time on the subject as Test captain, Cook confirmed the issues between Pietersen and the England team are still unresolved. But Cook is hopeful of a solution that will see Pietersen return to the England fold.
England and Wales Cricket Board chief executive David Collier and cricket managing director Hugh Morris have been in Sri Lanka, where Pietersen is working as a television pundit for the Twenty20 World Cup.
"I did have a meeting with Kev and I have been involved in meetings. Clearly the issues haven't been resolved and that is why he is not available for selection at the moment," Cook said.
"Time hopefully will be a healer and we will be able to move on."
Cook conceded England's hopes of winning the four-Test series in India have been hit by Pietersen's absence.
"He will be missed but it gives opportunities to other players and they can do well. There is no reason these guys can't fill the gap there," Cook said.
Meanwhile, former England captain Andrew Strauss has admitted it was important to discuss the incident with Pietersen.
He told Sky Sports News: "He apologised for a few things he had done and we are absolutely fine going forward."