The Premier League leaders have taken the first steps towards capturing the Juventus striker in the forthcoming window.
Goal understands that the Gunners have made preliminary contact with Llorente's representatives in a bid to secure proven back-up to spearhead Olivier Giroud for the second half of the season.
Arsenal are also keeping close tabs on a second Serie A forward, Stephan El Shaarawy, although his club AC Milan are only likely to sell in January if they get eliminated from the Champions League before Christmas.
Arsene Wenger’s priority remains to capture a marquee striker after moves for Luis Suarez, Gonzalo Higuain, Stevan Jovetic and Wayne Rooney all fell through last summer, while the Gunners were also unable to agree a last-ditch loan deal for Chelsea’s Demba Ba.