The Serbia international has rejected the chance to extend his stay with La Viola beyond 2023 and is expected to be lured elsewhere next summer.
A January exit for Vlahovic has also been mooted, but Fiorentina are thought to be after a £55m figure to sanction an exit midway through the season.
The report adds that the Gunners came forward with a new-and-improved offer for Vlahovic, but the 21-year-old wants to remain with Fiorentina for the rest of the season.
Vlahovic has 14 goals to his name from 16 appearances in all tournaments this season, including his side's second in a 3-1 Serie A win over Sampdoria on Tuesday. body check tags ::