Mbappe, 22, can sign for a new club on Jan. 1, as he will be a free agent next summer, and Madrid president Florentino Perez said on Tuesday he is optimistic in securing the forward's signature on a pre-contract next year.
However, in an interview with Le Parisien on Thursday, Lamari said her son is in negotiations over a new deal.
"We are talking right now with PSG and all is well," Lamari said when asked about her son's future.
"I spoke last night with [PSG sporting director] Leonardo. Will we reach a solution? One thing is clear. He is going to give everything until the end to win the Champions League."
Lamari said her son will make a decision based on his happiness.
"Kylian needs to be happy. If he is sad, he is capable of saying, I give it up," she added before joking: "And he says that often. With Kylian, everything can change from one day to the next."
Sources in Madrid previously told ESPN that PSG rejected a €200m offer from Madrid on transfer deadline day despite Mbappe having made it clear he did not wish to renew his contract at the Parc des Princes.
On Thursday, Leonardo said he has been angry with Madrid's ongoing pursuit of Mbappe, adding it shows a "lack of respect" towards the French club.
"In the same week, we've had a Real Madrid player [Karim Benzema], the coach [Carlo Ancelotti] and now the president of Real Madrid speak of Kylian as if it was their own player ... it's a lack of respect that we can't tolerate," Leonardo told L'Equipe.
"Kylian is a PSG player and the club understands perfectly that this relationship will last."
French media have reported that PSG are working on making Mbappe a new offer that would make him the highest paid player at the club, above Lionel Messi and Neymar.
Mbappe, who is on international duty with France, has not ruled out remaining at PSG.
"It's a club that's given me a lot," he said. "I've always been happy during the four years I've been here and I still am."
Mbappe joined PSG from Monaco in 2017 in a €180m deal, despite interested from Madrid.
A World Cup winner with France in 2018, Mbappe has won three league titles during his four years in Paris and finished as Ligue 1's top scorer three seasons in a row.
He has scored four goals and set up five more in 11 appearances in all competitions for PSG this season.