The Blues turned to Garner after their pursuit of Monaco's Lamine Camara collapsed in the closing stages of the window, with Chelsea having already sanctioned Enzo Fernandez's £125million departure to Manchester City in anticipation of a replacement arriving.
Garner, capable of playing in midfield or at right-back, appealed to Alonso as a versatile option, but Everton refused to entertain a sale so late in proceedings.
The 25-year-old England international only signed a new contract at Hill Dickinson Stadium in January, running to 2030, and is understood to be settled on Merseyside under David Moyes.
Chelsea's willingness to pay £65million, more than the £47million they had agreed for Camara, reflects both the urgency of their situation and the regard in which Garner is held following his rise from a squad player to a first-choice midfielder since leaving Manchester United in 2022.
Garner's route to first-team football took in loan spells at Watford and Nottingham Forest, with the second proving transformative as he helped Forest win promotion through the Championship play-offs. He joined Everton on a permanent basis and has since established himself as one of the more improved performers in the Premier League, a rise in stock reflected directly in the fee Chelsea were prepared to offer for a player City had considered unremarkable only a few years earlier.
Chelsea now enter the new season without a direct replacement for Fernandez, leaving Moises Caicedo, Reece James, Romeo Lavia, Jordan Henderson, Malo Gusto and Valentin Barco as the club's central options.
Everton, meanwhile, emerge from a chaotic deadline day having also missed out on Folarin Balogun, but with the satisfaction of having kept hold of a player considered central to their own midfield plans.
Chelsea's approach for Garner was reportedly one of several midfield options explored in the window's final hours, alongside interest in Roma's Manu Kone, whose move was blocked by the Italian club.
The Blues had generated significant funds through player sales over the summer, banking close to £384million before add-ons and sell-on clauses are factored in, giving the club's ownership group BlueCo the financial firepower to move quickly had Everton shown any willingness to negotiate on Garner in the final hours of the window.