After their emphatic FA Cup win over Manchester City on Sunday, the youngster believes the Blues can still challenge for trophies this season
The 20-year-old looped in a late header to cap an emphatic victory for the Blues at Stamford Bridge against an inexperienced team fielded by Manuel Pellegrini in Sunday's fifth-round clash.
Chelsea's Premier League title defence derailed during a dismal first half of the season under Jose Mourinho but, with their FA Cup and Champions League campaigns still alive, Traore is confident they can get their hands on some silverware this term.
"Chelsea were the champions last season so of course we can win any competition," he told Chelsea TV. "We just have to push a little bit more and keep fighting for each other.
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"I like challenges so I am always ready to come on the pitch and show what I can do so I always train for this kind of moments.
"It is a privilege for me, coming from Africa as a young player and being coached by a great manager like Guus Hiddink so I am proud of that."
Chelsea will meet Everton in the quarter-finals.