The Juventus forward has barely featured for Juventus since his free transfer switch in the summer, and the report claims he's on Arsenal's list of potential January window targets.
Arsene Wenger is looking for top tier players to carry Arsenal's momentum into the New Year following their strong start to the Premier League season.
The Gunners currently sit top of the table, two points clear of Chelsea and Liverpool. But they're short of options up front, with Frenchman Olivier Giroud the club's only recognised senior striker.
Which makes a move for the 28-year-old Llorente appealing for Wenger. Arsenal reportedly believe he's interested in a move to the Emirates Stadium, and have been tipped off to his potential availability on loan in the January window.
A loan deal would suit both parties - Llorente wants regular first-team football heading into a World Cup year with Spain while Arsenal will favour a loan move because January targets are likely to be cup-tied in the Champions League.
A temporary switch also allows Wenger to continue to explore big-money options for a summer deal - Luis Suarez remains a target for the Gunners boss.