However, it appears neither side earmarked the former Bilbao star as their number one forward priority.
United are yet to sign a striker despite sending Radamel Faclao back to Monaco (and subsequently Chelsea) from his loan spell and selling Robin van Persie to Fenerbache.
Manager Louis van Gaal is expected to land a forward if he offloads Javier Hernandez, who is valued at £12m and wanted by Tottenham and West Ham.
GETTY
Fernando Llorente helped Juventus win the Italian Super Cup in China earlier this month
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Meanwhile, Arsenal boss Arsene Wenger has already conceded he will sign a player if the deal is "exceptional", with many claiming that man would be Real Madrid forward Karim Benzema.
However, the £46m Real want for the France international has stumped the Gunners, leading to Llorente emerging as a possible alternative.