The 22-year-old, who began his career with Real Madrid, is out of contract at the end of the season and a new deal has yet to materialise.
Alonso cost around £2m in 2010 but has only this season cemented a regular place in the first team, his current six-match run the best of his Wanderers career so far.
Manager Dougie Freedman told Bolton's Twitter feed: "We received a bid for Marcos Alonso from Fiorentina yesterday and didn't feel it was enough. We let Marcos know and rejected it."







