The Brazil international has endured a mixed season under new manager Jose Mourinho, scoring eight goals and making two assists in 30 Premier League games.
Paris Saint-Germain, who have been courting Blues forward Eden Hazard, have been linked with a £42m swoop for the 22-year-old in recent weeks.
However, Oscar wants to remain at the Blues and emulate legend Didier Drogba by inspiring the west London side to a trophy-laden period.
“Didier has always been my idol,” Oscar is quoted as saying by the Daily Mail.
“Now I am wearing the same jersey he used to have. I am writing my own Chelsea story.”
Meanwhile, Jose Mourinho appeared to hit out at some members of his squad after a surprise 1-0 loss at Crystal Palace on Saturday.
“You see the matches we lost, except Villa, and you try to find points in common,” said Mourinho. “Stoke City away, Everton away, Newcastle away, Palace away, West Brom away when we lost two points, you try to find points in common and you find.
“Branislav Ivanovic, Gary Cahill, John Terry, Cesar Azpilicueta perform in the rain, the sun, big pitches, small pitches, aggressive teams, not aggressive teams. They perform every game from day one to today.
“Clearly we have some players who, because of their profile, find it difficult to perform in some matches.
“They are fantastic in some matches but they disappear in other matches. You can find easily in these matches something in common.”
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