"My contract expires in June but I definitely want to play here for another year," he told the club's official website.
"I was at West Ham for four years and I wanted to finish my career there, but that couldn't happen.
"My priority now is Charlton.
"I know the manager and the staff now and we are a very tight unit. We work hard but we have a lot of fun too. There is the perfect mix here.
"I feel like I am back in top form now and I think I've showed that I can give something to the team, not just during games but also in training.
"I'm not in the situation where I can demand a new contract. I've had a great season here - I hope we can finish even stronger - and I would love to stay here. The atmosphere is nice. And if we could qualify for Europe for the first time I would be able to write my name on a fantastic year for Charlton - I would be a part of something special."
He added: "If I don't get the chance to stay, I will thank everyone here from the chef to the kit man. I've had a fantastic season, not only on the pitch but also in my lifestyle.
"I don't have a crystal ball so I don't know if I will be here next season, but I hope that I am.
"My head tells me: 'if you stop Paolo, you are crazy'."