The north London side sold Robin van Persie to Manchester United in the summer and Arsene Wenger is said to be keen to find a long-term replacement for the Dutch maestro.
A number of names including Adrian Lopez, Abel Hernandez and Stevan Jovetic have been touted as potential transfer targets for the Gunners, however the French coach is an admirer of Llorente.
The Spain international has been a major player for Bilbao in their recent successful campaigns, with the San Mames club making the final of the Europa League and Copa Del Rey last season.
Llorente is in the last year of his contract with the Basque club, and has stated that he wants to move to a side playing Champions League football.
Although Juventus are also interested, Arsenal are ready to launch a January bid for the forward.