According to the Daily Mail, Wenger will be handed a £35m transfer budget, and the Gunners boss has his eye on a number of striker targets.
Following the departure of Robin Van Persie, a world-class replacement is thought to be Wenger's top priority, and the Arsenal boss has reportedly drawn up a transfer wishlist, with Llorente topping the bill.
The Athletic Bilbao striker has fallen out of favour in northern Spain after a disagreement with the Athletic coach Marcelo Bielsa.
The Spain international is out of contract at the end of the season, so would likely be an affordable target for Arsenal. The 27-year-old has 21 caps for Spain, and was part of the team that won this summer's Euro 2012 tournament, and the World Cup two years earlier in South Africa.
But Arsenal are also exploring alternatives should Llorente decide to move elsewhere. Chelsea, Manchester City, Juventus and Liverpool have been linked with the Bilbao striker, which could spark a bidding war when the transfer window reopens.
The Arsenal boss may look to move for Manchester City target Stevan Jovetic, or Llorente's Spanish compatriot Adrian Lopez. Lopez currently plays for Atletico Madrid, and has reportedly been extensively scouted by Arsenal coaches.
Chelsea were thought to be considering a move for Llorente, but their main transfer target is now believed to be Radamel Falcao. The Stamford Bridge side face a fight with Manchester City for the Colombian international, and Atletico Madrid have said Falcao could leave Spain for £48m.
Chelsea are believed to be keen to draft in another world-class striker, following a big-name departure of their own. Didier Drogba left Stamford Bridge in the summer, leaving Chelsea with Fernando Torres and Danny Sturridge as the club's only senior strikers.