The Serie A champions are hunting for a new boss after parting ways with Massimiliano Allegri.
The Bianconeri board reportedly view Klopp and Manchester City manager Pep Guardiola as ideal - albeit less realistic - options, but the German removed all doubt about his future as he focuses on this weekend's Champions League final.
"There's nothing true about it, I'm not going to leave Liverpool.
"I know Serie A very well, I follow it and I like it but I am going to stay at Liverpool."
Liverpool will hope to be crowned European champions for the sixth time when they meet Premier League rivals Tottenham at the Wanda Metropolitano on Saturday.
The Reds lost 3-1 to Real Madrid in last year's Champions League final, a defeat that was catalysed by a horror performance from goalkeeper Loris Karius.
The German 'keeper made an errant pass that allowed Karim Benzema to give Real the lead shortly after half-time in Kyiv, before allowing a long-range strike from Gareth Bale to fall through his hands to wrap up victory for the Spanish giants.
The Reds are looking to assuage the disappointment of missing out on the Premier League title to Manchester City on the final day of the season.