The Bianconeri face the Blancos at the Santiago Bernabeu on Wednesday in the third Champions League gameweek, as Antonio Conte's men continue to search for their first win in the competition this season following consecutive draws.
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"Yes, there was real interest," Llorente told AS. "In the end the timing wasn’t right, and something else came along.
"They tried to sign me at least twice. At first because it was impossible to leave Athletic. Over there, either someone pays your buyout clause or you stay.
"The last time was when I had a year left on my contract, the year we had a good run in the Europa League [2011-12]. As my contract began to run out Madrid were no longer interested and Juve turned up and gave me more confidence. Joining Madrid was once a possibility, as they are one of the best teams in the world."
Llorente has struggled to impress since his move from Athletic during the summer transfer window - sitting behind the likes of Carlos Tevez and Mirko Vucinic at times and failing to score regularly when he does start - but he insists he has Antonio Conte's support.
"He told me to relax and reminded me it was him who signed me," he continued. "He knows I’ve had a tough year and I knew that it would take me a while to return to my peak level of fitness."
Juve sits second in Group B but only one point ahead of third and fourth place.
And Llorente said that the team are desperate to make amends for dropped points in Europe and Sunday's 4-2 defeat to Fiorentina.
"We’re going to go out feeling strong despite what happened in Florence," the Spaniard added. "We haven’t started too well in the Champions League, we’ve only drawn with Copenhagen and Galatasaray, so we are hungry for the points and we need to pick up points from these two games with Real Madrid."