Morata has 10 Premier League goals in 19 appearances since joining from Real Madrid previous year, but after failing to find the net with simple chances against Stoke City in Chelsea's 5-0 win on Saturday, he has not enjoyed the festive season.
However, Conte insists he rarely aims high with his requests, as he hardly gets the players he wants.
Chelsea reportedly missed out on a number of players last summer, including Romelu Lukaku, Ross Barkley, Alex Oxlade-Chamberlain, Virgil van Dijk and Alex Sandro - all of which either moved to other clubs or didn't move at all.
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"I'm enjoying a lot staying with my players during training and in games".
"I think I am well trained for this but to play every three days is a big effort not only for my players but also for me", said Conte. I can give my opinion but the club decides on the players they want to buy, or invest in. Talking about Luiz first, the Brazilian has completely fallen out of favour with Antonio Conte and has seen Andreas Christensen talking his place while recovering from his injury.
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Speaking to Italian reporters after the game, as quoted by Football Italia, Conte revealed he has been hard done by when it comes to being delivered the players he felt he has needed in his career.
But Conte said: "My expectation for all the players we have in the squad is to stay here and to try to continue to work".
Conte says his participation on transfers is limited to making suggestions to director Marina Granovskaia, who leads on recruitment. I'm only a coach. I'm very focused on the pitch to try to improve my players and the transfer market is for the club.
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"If the club chose to ask me something about my team I will try to give my opinion".