The batsman was recently recalled to the squad for the upcoming tour of India after he was dropped for sending text messages to South African players during this summer's Test series.
"I think it's been a difficult two months for us as an England side, but as captain the best possible outcome is that we have a world-class player back in the team," Cook told Sky Sports News.
"Kevin is very contrite and desperate to be back playing and scoring runs for England. As captain that's all I want."
England fly out to India on Thursday ahead of a three-day training camp at the International Cricket Council Global Cricket Academy in Dubai.