PSG and the Premier League side have both been linked with the young forward in recent weeks but Mbappe says he intends to remain with Monaco.
The striker, who has scored three Ligue 1 goals in 11 outings this season, wants to repay the faith shown in him by Monaco amid claims of a 40million euros offer from Pep Guardiola's Man City.
"No. Even if anything can happen in football, I am very attached to Monaco," Mbappe told Le Parisien when asked if he could leave Monaco.
"This club has helped me to develop and gave me the opportunity to play football professionally. I hope to repay their confidence in me by being decisive on the pitch and winning titles."