The 21-year-old Argentine player has fallen out of favor at Manchester United after a disagreement with manager Ruben Amorim following their loss to Tottenham in the Europa League final.
Chelsea had previously shown interest in signing Garnacho in January but were rejected by Manchester United, who did not want to sell him to a rival mid-season.
Garnacho is understood to want to stay in the Premier League and compete in the Champions League.