The France international netted 15 times to help his side to their first top-flight silverware in 17 years, including the breakthrough strike in the title-clinching win over Saint-Etienne on Wednesday night.
Mbappe's form both domestically and in Europe this term has seen him touted with a number of heavyweight clubs, not least Real Madrid who are said to be prepared to spend big to land him, but the 18-year-old believes that there is more to come for both him and Monaco.
A year on from competing in the Coupe Gambardella, a tournament for Under-19s players, Mbappe is refusing to get carried away by the speculation.
"After the victory in Gambardella, my mother told me, 'It's all very well, but it's with the kids," The Sun quotes him as saying. "I replied: 'Look, give me a year and I will do the same with the adults.'
"For next year, I promise a better season. We must always set the bar high, otherwise we do not progress."
Chelsea, Manchester City and Manchester United are the other sides rumoured to have shown an interest in Mbappe, who has 26 goals and eight assists in all competitions this term.