The Premier League club are keen to secure the services of the 23-year-old full-back, who spent the second half of last season on loan at the Stadium of Light.
However, the player’s father and agent Marcos Alonso Senior has confirmed his son will return to the Florence club, where he still has two years remaining on his contract, as he awaits a decision on his future.
Alonso Snr told www.firenzeviola.it: "Marcos, after playing for six months without missing a game, is excited and very ready to get back at the coach's (Vincenzo Montella) disposal.
"Now it's up to Fiorentina to make a decision."
Reports have suggested Sunderland could use former Lazio defender Modibo Diakite as a makeweight in any deal, but Alonso Snr added: "Right now, we only know that he (Alonso Junior) was summoned by the club to begin preparing, and he still has two years of contract with the club.
"He starts with determination, but I repeat: Fiorentina will decide. We are available."