The France Under-21 international has verbally agreed terms with the Blues and wants to move to Stamford Bridge this month.
Lyon want to keep Gusto until the end of the season, but Chelsea are pushing to sign him now, and are ready to take their spending since last summer close to £500million.
Gusto is an attacking right-back, with similar athletic attributes to Reece James. He made his debut for Lyon as a 17-year-old in 2021 and has played 15 times in Ligue 1 this season.
Chelsea have made signing a new right-back to provide cover for James a priority.
Gusto has 18 months left on his Lyon contract, so will enter the final year of his contract in the summer, and Chelsea are working to agree a deal in the final week of the window.
Chelsea are also set to reopen talks to sign Benfica midfielder Enzo Fernandez. Talks broke down earlier this month, but personal terms are in place with the Argentina midfielder, who was one of the breakout stars of the World Cup.