Brazilian international believes the Blues' players must push hard until the end of the season if they want success despite congested schedule over the Easter period
The Blues face Tottenham in the FA Cup semi-final at Wembley on Sunday before taking on Barcelona in the Champions League last four next week.
Luiz believes the club's top players must continue to perform at a high level if they want to win trophies despite games coming thick and fast at this stage of the season.
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He told reporters: "Chelsea want to win all the competitions. I think we will put the best team against Tottenham, the best team against Barcelona.
"It's impossible to rest too much now. It's a short time between games because Chelsea compete in three competitions.
"Other teams have more time as they are not in the competitions. It's normal.
"We have the opportunity to win the FA Cup and the Champions League. This is football at the top level and we are prepared for the games."