Llorente is currently on holiday with his family and reports emerged on Thursday that he had suffered an injury in the incident in Italy.
Swansea have revealed that the Spaniard has suffered a fractured arm, but they remain hopeful that he can still appear during the opening weekend of the Premier League in the middle of August.
A club statement read: "The 32-year-old suffered the accident while cycling on a family holiday, and despite it not being a serious break that requires an operation, it does mean the club will have to tailor his pre-season training accordingly.
"The club remain optimistic that he will be available for selection for the first game of the Premier League season against Southampton on Saturday, August 12."
Last season, Llorente scored 15 goals from 33 top-flight appearances as he helped the club to avoid relegation to the Championship.