This is according to Marca, who report that the Blues are ready to pay the €25million price tag for the former Bolton man.
Primarily a left-back, Alonso played 31 league games for Fiorentina last season, amassing a combined seven goals and assists.
Having been linked with Alessio Romagnoli, and having offer after offer rejected for Kalidou Koulibaly, Chelsea have turned to Fiorentina for rearguard cover.
La Viola would make a tidy profit on Alonso should the deal go through, having picked him up for free back in 2013.
Conte re-iterated his desire to bring in a new defender after Chelsea’s 2-1 win at Watford.
“If you look now at our squad, we have only five defenders” he told Sky Sports, “four that started today and an academy player, Ola Aina. He has great potential, but with any young player you must work to put them in the first team.
“If one defender is injured or banned, then we are in trouble, but the club and me we know this and we are talking every day to improve the squad.
“We know that this market is very difficult. It’s crazy. I don’t want to buy only to buy. I want to buy the right profile for Chelsea, the right investment for the solution and for the future.”