Mbappe, who joined PSG from Monaco in 2017, last week won the Ligue 1 Player of the Year prize and comes into the final weekend of the season as the division's top scorer with 25 goals.
Rumours are swirling in France and in Spain about when he will confirm where his next contract will be.
"Mbappe, end of the suspense on Sunday," claimed the headline in French sports daily L'Equipe on Friday.
Mbappe's mother told Egyptian media that her son had offers from both clubs and was still weighing up which one to accept.
"All the negotiations are finished. We have an agreement with Madrid and Paris. Now it is up to Kylian to choose," Fayza Lamari told Kora Plus.
In Spain there is nevertheless still optimism that he will choose to continue his career with Real.
"I think he will be at Real Madrid, but just as one day is white and the next is black, things change," La Liga president Javier Tebas told sports daily Marca.
"But I think he will be."
Pochettino said he hoped the 23-year-old would remain at PSG even if uncertainty surrounds the coach's own future despite the Argentine and his staff having a year left on their own deals.
"I hope Kylian is still here for many years to come but I also can't lie. I don't know what is going to happen," he said.
"We have a year left on our contracts so we will potentially be here next season. I just hope tomorrow (Saturday) we can enjoy celebrating the club's 10th league title."
One player who is definitely expected to move on is Angel di Maria, with the 34-year-old Argentine winger's own contract expiring and PSG understood to be happy for him to leave.
PSG have cantered to the Ligue 1 title, equalling Saint-Etienne's French record for most league championships, but their season has been soured by defeat against Real Madrid in the Champions League last 16 in early March.
The Parisians were 1-0 up away to Madrid an hour into the second leg thanks to a Mbappe goal, and led 2-0 on aggregate, only to implode and go out to a Karim Benzema hat-trick.
"I hope the best is still to come. I think everyone at Paris Saint-Germain wants to win the Champions League. That has become an obsession for this club and I hope we can win it," Pochettino added.
"That spell in the second half in Madrid saw us not get the result we wanted and created lots of questions and emotions that we have not been able to control in recent months. Despite that the players deserve to be congratulated because they have shown the ability to lift themselves and finish the season."