Big-spending Paris Saint-Germain are among those reported to be keeping a close eye on Oscar's progress, but the 22-year-old is enjoying his time under Jose Mourinho.
He said in the Daily Star Sunday: "Jose (Mourinho) has shown me I can be one of the best.
"The manager has given me this confidence and I have grown better and better under him. Now I just hope I can keep on getting better and win titles with him at the end of the season.
"The team is top of the Premier League and the manager has his own way of playing. He alternates quite a bit because we have a lot of games.
"But that's normal. I'm playing well at Chelsea and am in my prime right now."
With Oscar seeing his long-term future at west London, he hopes he can make a similar impact to that made by a former owner of the number 11 shirt.
He added: "Didier (Drogba) was always an idol.
"I'd watched him lots on the TV and then suddenly I was wearing the same Chelsea jersey he always wore. I feel very proud about that.
"But I am writing my own story. I have my own style and hopefully I will be able to have my own great story at Chelsea - just like he did."