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Barcelona received £37.5million transfer offer for Malcom from Borussia Dortmund.
Arsenal have been long-time admirers of the Brazilian and attempted to land him from Bordeaux before he completed his move to Barcelona 12 months ago.
According to Goal, Borussia Dortmund are in advanced talks with Barca over a €42m (£37.5m) deal for the Brazilian.
The deal would be around £1 million more than Barcelona signed him for one year ago.