The 21-year-old Argentine player is reportedly seeking a move to Stamford Bridge due to a disagreement with his manager, Ruben Amorim.
Manchester United values Garnacho at £50 million, while Chelsea is only prepared to pay £30 million for his services.
Despite Garnacho's impressive performance for United last season, scoring 11 goals and providing 10 assists in 58 games, Chelsea remains hopeful that United will eventually sell him for a lower price.