Spanish outlet Don Balon, as quoted by the Daily Star, is reporting that the west London side have tabled a big-money offer to try and convince the Belgian to sign for the Blues this summer.
The same report states that Carrasco looked set for a move to Bayern Munich but Atletico Madrid’s transfer ban has affected that proposal.
It is claimed that Atletico Madrid’s move to sign Vitolo has cast doubt over Carrasco’s long-term future at the Spanish club, even though he’ll be loaned to Las Palmas until January due to their transfer ban.
The 23-year-old Carrasco scored 10 goals and made four assists for Atletico Madrid last season in the Spanish league.
He started 27 games in the top flight and made a further eight appearances from the bench.
Chelsea completed their third signing of the summer on Saturday when they finally announced a deal to land Tiemoue Bakayoko from Monaco, following the arrivals of Antonio Rudiger and Willy Caballero.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news