France international Mbappe revealed earlier this week he asked to leave PSG in July after deciding he did not want to extend his stay at the Parc des Princes.
The 22-year-old is due to become a free agent at the end of the 2021-2022 campaign and can sign a pre-contract agreement with a new club from 1 January 1.
However, Mbappe's mother has suggested there is still a chance the superstar forward could remain a PSG player beyond next year.
"We are talking right now with PSG and all is well," Lamari said.
"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."
Mbappe's revelation this week that he wanted out of PSG in the close season sparked fresh speculation over a possible mid-season switch to Madrid.
The Spanish side is reported to have had three bids turned down for the former Monaco man in July and August, the last one said to be worth up to €200million.
Speaking shortly after Mbappe's interview was published, Madrid president Florentino Perez said he was hopeful his future will be resolved in January.
PSG director Leonardo accused Madrid of lacking respect, but the decision over where Mbappe will ply his trade next season will ultimately come down to the player.
"Kylian needs to be happy," said Lamari, who handles her son's business interests. "If he is sad, he is capable of saying 'I give it up'. And he says that often!
"With Kylian, everything can change from one day to the next."
Mbappe has scored 136 goals in 182 games for PSG since joining from Ligue 1 rivals Monaco in August 2017 on an initial loan deal, which was made permanent the following year.
That tally is bettered only by Cristiano Ronaldo (149), now team-mate Lionel Messi (163) and Robert Lewandowski (191) across that period among players from Europe's top five leagues in all competitions.
Mbappe's 61 assists over the same timeframe is the sixth-highest total, meanwhile, with Bayern Munich's Thomas Muller leading the way with 75.
The 22-year-old has made a largely underwhelming start to the 2021-22 campaign, however, having scored only four goals in 11 appearances, though he does have five assists.
That includes a run of 17 shots without scoring in Ligue 1 since netting against Clermont Foot on September 11.