Media reports have linked the wealthy Ligue 1 leaders to Real Madrid coach Jose Mourinho for next season, however, Nasser al-Khelaifi said the Portuguese was not a target and it would be up to Ancelotti to decide if he stays at PSG.
"He will still be here if he wants to," al-Khelaifi told daily Le Parisien, three days after the Italian coach led PSG to the Champions League quarter-finals for the first time in 18 years.
"He has done an excellent job. It has been difficult from time to time because he has been under a lot of pressure, but he has done very well. Carlo is one of the best coaches in the world, if not the best.
"As for Mourinho, I don't know what his situation (at Madrid) is but it's none of my business," he added.
Al-Khelaifi, who took over as president when Qatar Sports Investment bought PSG almost two years ago, also dismissed reports Leonardo could leave the club and return to Italy where the Brazilian has worked as Inter and AC Milan coach.
"He is staying. I have a good relationship with him," he said.
"I hear things like 'sources in Doha have said there's a problem with Leo'. But people have to understand that I am Qatar's official voice here. Leo is doing a very good job."