It was recently reported that the 54-year-old had listed the Portuguese midfielder, who has made 56 appearances this season, as his main priority ahead of the transfer window.
Juve lead Serie A by four points with two games to go and are into a Champions League final against Real Madrid at the start of June.
According to an article in today's L'Équipe, AS Monaco manager Leonardo Jardim's future is now in doubt, and a move to rivals PSG can not be excluded as a possibility.
'I am finishing my third season in Monaco, who gave me the opportunity to play at a higher level, ' he told SIC.
The France worldwide 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 is the hottest property in Europe following a debut season that saw him net 25 goals for the French champions, all before his 19th birthday... "Mbappe, we all know he has qualities, but perhaps doing another year could be good for him, for Monaco and the France team".
AS Monaco has proven to be a very potent attacking side, scoring an fantastic 104 goals over 37 games in the league this season.
After finishing a whopping 31 points behind PSG in third place last season, Monaco completely turned things around to seal an eighth title overall.
The 18-year-old has lit up French football this season with his 15 league goals helping them to the French title, while another six goals in Europe meant Monaco reached the semi-finals of the Champions League.
Therefore their desire in competing with big-money merchants like Real Madrid and Manchester United to secure Mbappe's signature signals a step in the right direction as far as bringing in top quality players is concerned.
"But of course, every player dreams of playing for the best teams and in the best divisions one day".