Reyes rejoined the club he started his career with from Atletico Madrid at the start of the season.
El Confidencial report that the club and its President Jose Maria del Nido are keen to recoup some of the money invested in him.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.