The two clubs have been in talks for weeks with the 21-year-old pushing for a move to Stamford Bridge after a high-profile falling out with Ruben Amorim.
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According to Sky Sports, their ‘close’ to agreeing a deal for Garnacho after Chelsea submitted an offer of £35 million plus £5 million in add-ons.
United valued the Argentina international at £50 million but Chelsea are reluctant to meet that asking price.
Garnacho is understood to have turned down offers from several clubs throughout the summer as he has his heart set on a move to Chelsea.