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Crystal Palace sold their right-back Aaron Wan-Bissaka to Manchester United for the sum of £50m and are now searching for a replacement.
James excelled on loan for Wigan last season and was named in the Championship team of the season.
Palace have been rumoured to be interested in a number of names that will replace Wan-Bissaka, and the Chelsea academy product has caught the interest of Palace boss Roy Hodgson.
According to Starsport, Palace have submitted a bid of £20m for the 19-year-old, but the Blues rejected the offer. Chelsea see James as a youngster with high potential, and are unwilling to lose him.
James is currently recovering from ankle ligament damage he picked up while representing England under-20s at the Toulon Tournament, and he’s expected to be back by September.
Palace have been poor so far in pre-season as they suffered a humiliating 6-2 pre-season defeat at Barnet this week with another loss at Nottingham Forest on Friday.
Hodgson has now sent warning to the club board to sign a replacement for Wan-Bissaka ahead of next season.
“We’ve got enormous problems at the back at the moment,” he said.
“We really don’t have any defenders, to speak of.
“Aaron’s gone and we’ve got three others injured.
“We will have to do the best we can to make sure we replace [Wan-Bissaka] in some way.”