The Brazilian attacking midfielder recognises that, despite his £31.6 million transfer fee, he will have to tussle with the likes of Eden Hazard and Juan Mata for starts
The Brazilian moved to Stamford Bridge from Anzhi Makhachkala in August for a €37 million (£31.6m) fee after the Blues fought off Premier Leaugue rivals Tottenham and Liverpool for his signature.
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"I know that I haven't secured my spot here," Willian told Globo Esporte. "I'll do my best to achieve that place, while respecting the other players. I'll train, play and do my best to get the trust of the manager and of the fans."
The attacking midfielder explained that the chance to play under Mourinho, as well as link up with fellow Brazilians at Stamford Bridge, was a big part of his decision to join Chelsea.
"The Brazilians called me, especially David Luiz, who told me to come quickly," he added. "I was very happy to have them around and they will certainly help me a lot.
"I wanted to play at Chelsea, even more so now with Jose Mourinho, who is the best at what he does."