The video report claims Arsenal are tracking the out-of-favour Spanish international having failed to secure a big-name striker over the summer.
The Gunners were linked with the likes of Luis Suarez and Gonzalo Higuain, but their only spending consisted of the £42.4m allocated for Real Madrid playmaker Mesut Ozil.
With Olivier Giroud the club's only recognised centre-forward, Arsene Wenger is believed to be considering his options for the winter window.
Llorente, who moved to the Serie A champions in the summer, has failed to settle in Turin, although the club insist he is not for sale.
The Spain international has struggled for fitness and form, with Carlos Tevez and Fabio Quagliarella preferred against FC Copenhagen in the Champions League last night. Llorente was an unused substitute.
Arsenal are short of options with the squad down on numbers due to injury. Lukas Podolski is a long-term casualty while Alex Oxlade-Chamberlain is also sidelined for up to three months.