Llorente, 32, is likely to be part of the Spurs squad travelling to Turin to face the Italian champions in the first leg of the Champions League round of 16 this week. He spent two years at Juventus, scoring 23 goals in 66 league appearances, before moving to Sevilla in 2015.
The Spain international has started only one Premier League game for Spurs this season and was linked with a move to Chelsea in the January transfer window.
"Juve is a difficult place to leave. I left the Vinovo training ground crying," Llorente was quoted as saying by the Daily Mirror.
"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."
Meanwhile, Juventus are sweating over the fitness of Argentine forward Paulo Dybala, who has been out of action since early January with a thigh injury.
Spurs boss Mauricio Pochettino said he hoped for Dybala to play so his team has the opportunity to face "one of the best in the world".
"I think Dybala will recover and I hope he does, because I think it's always nice to play against the best in the world," Pochettino was reported as saying by Football Italia.
"I put Dybala in that category, because he is a special talent and seeing him on the pitch is wonderful, even if he might cause your team a few problems."
Juve host Tottenham in Turin in the Champions League round of 16 first leg on 13 February, with the return leg scheduled for 7 March.