According to reports from France, the 22-year-old has little intention of signing a new long-term deal at the Parc des Princes.
That would mean Mbappe being allowed to enter the final 12 months of his existing deal by the time this summer's transfer window opens.
Real Madrid have been tipped to move for the French World Cup winner, but Pochettino will not let arguably his biggest asset leave without a fight.
"I'll fight with all my energies to keep Kylian here at PSG," he told Spanish radio show El Larguero.
"PSG are doing everything possible to keep Neymar and Mbappe. I am equally optimistic that Mbappe will stay. They both have a huge commitment."
Neymar is also set to enter the final year of his contract and reportedly has a fortnight to make a decision over his future, with Barcelona monitoring developments.
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