The former Stoke forward, whose contract expires at the end of next season, insists that the side are entering an exciting period under manager Michael Appleton, who replaced Steve Cotterill in October.
"I'm a big fan of the direction Michael is trying to move this football club in," he said. "It's exciting. He has got the team organised, we are creating chances and the main thing is he has got the players on board.
"It's an important period on the playing side. In the next few years, this club – if it can stabilise behind the scenes – has as good a chance as any of achieving things.
"I want to be part of that, even beyond what I have on my current contract. There is no reason on earth why I would ever want to leave this football club."
Kitson, who arrived at Portsmouth at the start of last season, has scored 11 goals in 46 appearnaces for the South Coast club.