Pochettino recently stated Mbappe will '100 per cent' remain in the French capital next campaign.
The 23-year-old is out of contract with the Parisians in the summer, and has been widely tipped to make the move to Real Madrid.
Ancelotti was asked at his pre-match conference on Friday ahead of Los Blancos' LaLiga clash against Espanyol what he made of Pochettino's comments.
"Pochettino said Mbappe will 100 per cent stay? Sometimes coaches at a press conference cannot tell the whole truth," he said, laughing.
"I think all the Madridistas are thinking about LaLiga and the Champions League right now. Only about that."
This then forced Pochettino to come out and clarify his comments before his side's game with Strasbourg on Friday night,
"I said me and Mbappe will 100% stay at PSG next season? No… I was talking about the present", Poch told Prime Video
Mbappe's contract runs out at the Parc des Princes on June 30, and he is expected to move to the Spanish capital, with no agreement yet reached over an extension.
The France international met with PSG officials in Qatar recently, and his mother was also present for talks alongside club president Nasser Al-Khelaifi.
Mbappe publically stated he could put-pen-to-paper on a new deal after helping side to a 5-1 win over Lorient at the start of the month.
"Is staying at PSG is possible? Yes of course", he told reporters at the time.
Meanwhile, Pochettino ashed speculation over his own future, with reports suggesting PSG could sack him following their Champions League exit at the hands of Real Madrid last month.
Asked how likely it is the French champions will keep him on as head coach and manage to tie Mbappe down to a fresh deal, the Argentinian boss said in his press conference on Thursday: "100 per cent in both cases."
"It's my feeling today, what I perceive today. That's what I can say now.
"Of course, it's football and you never know what can happen. But when asked on what I think today, that's my answer."