Muchova beat Sabalenka in a dramatic semifinal match
Radio stations France Info and RMC reported that PSG had agreed to pay 180 million euros ($215 million) including bonuses for the French international striker.
That would make him the second most expensive transfer in football history behind Neymar, who joined PSG from Barcelona for 222 million euros earlier this month.
Despite the reports, Mbappe was named on the Monaco bench for Sunday night's Ligue 1 meeting with Marseille.
According to sports daily L'Equipe, Paris will initially sign Mbappe, 18, on loan before making the move permanent.
"Monaco and PSG on Sunday reached an agreement for a loan deal for Kylian Mbappe to the Parisian club with an option to buy for 180 million euros," said L'Equipe, adding that Mbappe would undergo a medical by Monday morning.
A loan deal would help PSG get around UEFA's Financial Fair Play (FFP) rules, with many wondering how the Qatar-owned club can avoid sanctions from European football's governing body considering the investment already made on Neymar.
FFP rules currently stipulate that clubs cannot post losses of more than 30 million euros over the three-year period to 2018.
Among the sanctions risked by PSG if they are found to have broken those rules is a ban from the Champions League.
Mbappe burst onto the scene in the second half of last season and scored 15 goals in 29 appearances in Monaco's run to the French title.
Muchova beat Sabalenka in a dramatic semifinal match
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