The Premier League pair already had to contend with interest from Tottenham Hotspur and Real Madrid, and now the Blaugranas will likely make it even more difficult to sign the 30-year-old.
It is somewhat surprising that so many clubs are keen on the forward, considering he scored a paltry nine goals in 45 appearances last season. This is a massive drop off from the previous campaign, in which he netted 18 times.
Although the Spain international does contribute more than just goals, with hold-up play a big part of his game, the stature of the interested sides is still something of a surprise. It is unlikely that the former Athletic Bilbao man would be first choice at any of the clubs, with the possible exception of Spurs.
At Anfield, the Spaniard would likely play second fiddle to Christian Benteke, who recently signed for £32.5 million [BBC], and Daniel Sturridge, who will be hoping for a comeback season after struggling with injuries last time round.
Red Devils boss Louis van Gaal has already confirmed that Wayne Rooney will be his main striker in the next campaign [Sky Sports]. Having recently lost Radamel Falcao and Robin van Persie, a forward is needed at Old Trafford but they will likely find themselves behind the skipper in the pecking order.
Meanwhile, the aforementioned Liga BBVA outfits have two of the best front lines in world football, and Llorente may not even be able to get on the bench when their star-studded squads are fully fit.