The Sky Blues, under manager Frank Lampard, sit free and clear at the top of the Championship table.
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The Telegraph says Coventry want to further boost their title hopes with a move this month for Esse.
Esse, an England U21 international, joined Palace a year ago from Millwall, though has struggled for minutes under manager Oliver Glasner.
Coventry must see off competition to land Esse, though there is a belief they're in the box seat for the attacker.