Alonso is out of contract at the Reebok Stadium and he is set to leave the Championship club on a free transfer.
A number of teams, including Stoke and Hull City, have been linked with a move for the full-back, but Fiorentina are favourites to sign the Spaniard.
Fiorentina have held a long-term interest in Alonso and tried to sign him during the January transfer window.
The Italians are now hopeful that they have agreed a deal as they look to bolster their squad for next season.
Alonso cost Wanderers £2.5m when he signed from Real Madrid in the summer of 2010 and he made 46 appearances for the club during his time at the Reebok.