The 18-year-old starlet is enjoying a breakthrough season at the Stade Louis II but has been on the wanted lists of top clubs for a while, having been courted by Real Madrid and Zinedine Zidane when he was just 14.
Monaco's Champions League last-16 opponents Manchester City reportedly made a £32million approach for him in the summer, but Mbappe has no plans to leave the club just yet.
"Even if things can happen quickly in football, I'm very attached to Monaco," he told Le Parisien. "It's the club I’ve grown up at and has given me the chance to play professionally. I hope to pay back the club's confidence, to be decisive and to win titles."
In a further blow to the Premier League club's hopes of signing Mbappe one day, the teenager then revealed his desire to play for PSG in the future.
"What player doesn't dream of signing for PSG?" he admitted. "But today, I'm at a team that's really going well and I have no intention of leaving Monaco to help PSG.”
Mbappe turned down both PSG and Real Madrid earlier in his career and says he has no regrets about his decision to choose the principality club.
"PSG had contacted me but the project of Monaco suited me better," he added. "It allowed me to progress and to give me the best conditions on a sporting, education and human level. Now the politics at PSG have changed and the young players have more chance to play at the highest level."