The Spaniard was on the books of the Bianconeri between 2013 and 2015, scoring 27 goals in 91 appearances.
Since his time at Juve, Llorente played for Sevilla and Swansea City before completing a move to Spurs last summer.
However, the 32-year-old is currently on the fringes of the first team, having started just one Premier League game this term, and has scored just twice in all competitions.
Juve play Tottenham on Tuesday night in the last 16 of the Champions League and Llorente spoke fondly of the Italian giants, describing the club as a "family".
"Juve is a difficult place to leave," Llorente is quoted by The Mirror as saying. "I left the Vinovo training ground crying.
"It's also true what David Trezeguet said: 'It's only when you leave Juventus that you realise what you had'. I miss it like crazy and would love to return.
"It's a special club because, despite being an enormous club, it's like a family inside.
"There is a fine image of Juventus here and I raise it even more: I always speak very highly of the Bianconeri and give them a good rep."
Llorente, who was left out of Tottenham's squad for Saturday's 2-0 win over Arsenal, was linked with Chelsea in the January transfer window.