The experienced striker joined Chelsea on a one-year contract from Anzhi Makhachkala before the close of the summer transfer window and has scored six goals in 14 league appearances.
He started Monday night's 1-0 win at title rivals Manchester City, which moved Chelsea level with Manuel Pellegrini's side and two points behind leaders Arsenal.
Eto'o has won domestic titles with Barcelona and Inter Milan, and the 32-year-old is determined to complete his collection with a Premier League winners' medal.
"I had the chance to play in Spain, we won," Eto'o told Le Monde. "I had the chance to play in Italy, we won. And I hope that, thanks to God, I will also win a title in England. And I think my career will be complete."
The Cameroon international scored a hat-trick in last month's 3-1 win over reigning champions Manchester United, but Eto'o insists he did not need to prove he still retained his goalscoring instincts.
He added: "I have nothing to show. I'm Samuel Eto'o. And I do not think I have to show anything to anyone.
"I should rather try to take pleasure. Those who analyse football know that my performances are there.
"From the sidelines, I cannot show what I'm capable of. Jose knows what I can do on the pitch."
Eto'o had spent two years with Anzhi prior to joining Chelsea and he explained the reasons for leaving the Russian club, with Jose Mourinho's presence as Blues manager a big factor in his decision.
The forward continued: "Maybe I would not have joined Chelsea, however at the time of (Anzhi's billionaire owner M. Suleyman) Kerimov's problems we had to look at the possibilities that could be on the market.
"The Chelsea opportunity ended up presenting itself. Every great player who had a career like I had would have gone to a club like Chelsea.
"Jose weighed on my decision to come to Chelsea around 80% because I had worked with him at Inter Milan. This went extremely well. We had a fantastic team. That season [2009-2010] we practically won everything.
"Jose had already allowed me to make a good choice in summer 2009. A choice that was difficult because I left Barcelona and I had to choose the right club at a time when I had to prove that what I had in Barcelona was not an accident."