Romelu Lukaku scored four goals in Everton's 6-3 win over Bournemouth
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Costa was reportedly offered around £600,000 a week to quit Stamford Bridge for Chinese Super League club Tianjin Quanjian.
Costa is expected to leave Chelsea at the end of the season, with China his likely destination.
So Conte has lined up former Blues hitman Lukaku to fill the void at his old club.
But Lukaku is refusing to get carried away with his good recent form, insisting he is not falling into the trap of considering a big move away.
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Romelu Lukaku failed to make the grade under Jose Mourinho at Chelsea
“I’m just focused on this period of time and I don’t want to look ahead too far,” he said.
“That is the mistake I made last year. I was focusing already ahead and looking forward to things in front instead of the present.
“Now for me it is just game after game, day after day. Improve, come in, do my job and then go home to rest, work again on my body to recover and make sure I can play the next game. It is day by day now.”