Llorente played under Conte at Juventus and the Blues boss had tried to arrange a short-term deal for the Spain international in January this year to boost his side's chances of lifting the English title.
Swans boss Paul Clement chose to hold onto his target man, however, and Conte was keen to talk about his admiration of the 31-year-old as he aims to maintain his side's eight-point advantage in the league.
"I know him very well because Fernando played with me at Juventus," He said at a news conference at Cobham Training Ground. "We won together - he is a really good player.
"I have great admiration for him. As a player but also a man, because he is a great man. It is a great pleasure to see him tomorrow. I wish for him the best, but [only] after the game!"
Conte smiled when asked whether his side put in a bid for his former player during the recent transfer window, but refused to confirm the reports from January.
"This is the past," He said. "It is not right to talk about the past. Focus on the present. For sure, I have great admiration for him and we must pay great attention tomorrow, but I'll stop [talking about the transfer bid]."
"He had a great impact for the team and also with the transfer window. They reinforced the team and we must pay great attention tomorrow because for sure it will be a really tough game." He added.
"If you watch the game against Liverpool and Manchester City you understand the difficulty of the game, but I am sure my players understand this. We worked well to face them in the right way [before] but Paul Clement is doing a great job with Swansea.
"He's had a great impact. They are very compact defensively and dangerous in offensive situations and set pieces. We must pay great attention."