The report comes after the Primera Division club lost out on the signature of Neymar to rivals Barcelona, and have also been scared off by the valuation Tottenham Hotspur have placed on Gareth Bale.
Florentino Perez is keen to add a marquee signing during the summer transfer window, and now has his sights set on Mata, who has been linked with a move away from Stamford Bridge following the return of Jose Mourinho.
Spanish newspaper Marca reported earlier this week that Mourinho was prepared to risk the wrath of Chelsea supporters by selling Mata, along with his Spanish compatriot Fernando Torres, in a huge shake-up of the Blues first-team squad.
Mata enjoyed a scintillating 2012/13 campaign and was named Chelsea Player of the Year and Players' Player of the Year. He also led the Premier League assists table with 12 assists, and was named in the PFA Team of the Year to cap an impressive season.
With that in mind, it seems unlikely that Chelsea would be willing to sell Mata, particularly for less than the price they paid for the former Valencia star in the summer of 2011.
However, Sport says that the west London club would be willing to listen to offers of €35million, with Roman Abramovich likely to plough that money straight back into the Chelsea squad to help Mourinho with his overhaul ahead of the start of 2013/14.