Mbappe, who is into the final year of his contract in Paris, has long been courted by Madrid and the French star revealed he wanted to leave PSG for the LaLiga powerhouse at the start of the season.
PSG sporting director Leonardo last week slammed Madrid for their "not respectful" conduct in pursuing Mbappe for the past two years.
Leonardo was confident about the Parisians' chances of extending the 22-year-old's current deal, but Pochettino was less bullish in his assessment of Mbappe's future in the French capital.
"Mbappe is fine, he's a calm boy with a lot of personality and a very sociable character, he is clear about things and loves football, he's very mature for 22-years-old," Pochettino said in an interview with COPE and Radio MARCA.
"Kylian will make the decision he has to make and the club will do everything possible to keep him, because we're taking about one of the best players in the world at 22.
"I'm left with the fact that the situation is open and in the future anything can happen, the position of a few months ago may change in the future, PSG as a club certainly have the ambition and ability to persuade him and offer him things so that he can stay and be happy, the possibilities that he could change his mind are there."
Pochettino also offered an update on former Madrid captain Sergio Ramos, who joined PSG on a free transfer in the off-season but is yet to debut due to injuries.
The 35-year-old is closing in on a return to fitness after a frustrating start to life in Paris.
Ligue 1 leader PSG plays Angers on Saturday, before meeting RB Leipzig in the Champions League on Wednesday.
"Unfortunately, Ramos hasn't started training with the group yet, but he is close," Pochettino said.
"We're happy with his progression, he's a great champion and someone who isn't going to doubt his qualities and footballing talent, he's not having a good time right now but he is strong."