Pochettino's future in the French capital has been shrouded in doubt ever since PSG were knocked out of the UEFA Champions League by Real Madrid at the round of 16 stage.
The former Southampton and Tottenham Hotspurs boss has however guided the Parisians to their 10th Ligue 1 title.
Mbappe's contract expires this summer and he has been linked with a move to Real Madrid, whose bid for the 23-year-old was turned down last summer.
Pochettino believes he and Mbappe will not be departing the Parc des Princes come the end of the season.
Ahead of PSG's upcoming game against Strasbourg, Pochettino was asked at a news conference what percentage he would give himself and Mbappe staying at PSG next year, he said: "One hundred per cent, in both cases."
"That is how I feel today. That is what I can say to you today. I can't say anything else. That is how I feel right now.
"This is football, and we never know what might happen."
Pochettino added on his relationship with the PSG hierarchy: "There haven't been any concrete talks, beyond what is normal in terms of our plans with what we have been doing so far.
"We have a natural relationship, we communicate regarding different topics. Of course, they change depending on the circumstances at the time, but the relationship and communication are good.
"We keep working hard, not just bearing in mind the present, but also with the responsibility to think about the future, so that is what we are doing."
