Both men have been heavily linked with summer moves to Madrid, with the Blancos forced to deliver public denials of bids being tabled.
PSG have maintained throughout that they have no intention of parting with any of their prized assets, with €222 million (£196m/$261m) invested in luring Neymar away from Barcelona in 2017.
He saw his debut campaign in France ended by injury, before struggling to produce his best at World Cup 2018, and those at Parc des Princes are convinced he will be back on their books determined to prove a point in the upcoming campaign.
"He wants to succeed, after not achieving much at the World Cup. I think he wants to win titles with PSG."
The 19-year-old striker helped France to claim a second World Cup crown, with his pace, neat footwork and eye for goal landing him the Best Young Player Award.
Talk of a move to Madrid has built on the back of those efforts, but PSG have taken up the €180m (£159m/$211m) option in his loan move from Monaco and are looking forward to being the ones to benefit from his ongoing development.
Fernandez added on Mbappe: "He will also stay.
"He has said it, 100 per cent. He wants to win the Champions League with PSG.
"[FFP] does not worry me. The important thing is that both Neymar and Mbappe want to stay at PSG."
PSG are currently preparing to open their International Champions Cup campaign, where they will face Bayern Munich, Arsenal and Atletico Madrid, before starting the defence of their Ligue 1 title against Caen on August 12.