The Gunners offloaded Torreira on a loan deal during the last transfer window, with the Uruguay international heading to Spain to link up with La Liga giants Atletico Madrid.
However, Torreira has struggled to make an impact in the Spanish capital and has been linked with potentially cutting the loan short.
The former Sampdoria man had interest from Italy in the summer and is still a wanted man in Serie A, with Fiorentina one of several clubs to have cast admiring glances.
And, according to Italian daily La Nazione, Arsenal are ready to speak to Fiorentina about Torreira.
The Gunners are ready to acknowledge that the midfielder may need to move again this season and Serie A could be his destination.
Fiorentina have made Torreira a priority target as they look to add a midfielder to the ranks.
Torreira has clocked just 200 minutes of football in La Liga this season, and only seen 32 minutes of action in the Champions League.
The Uruguayan was looking to play on a regular basis under Diego Simeone.
