Mbappe is running down the final few months of his contract with the Ligue 1 champions, who have now been informed that he plans to leave when his deal runs out at the end of the season.
The 25-year-old has been free to discuss pre-contract terms with foreign clubs since the start of January, and he is now believed to have given Real Madrid his word that he will be moving to the Bernabeu this summer.
PSG had always retained hope of extending Mbappe's terms before receiving word from the France international that he planned to depart earlier this month, and head coach Luis Enrique has all but confirmed his imminent exit.
After benching Mbappe for their 2-0 win over Nantes two weekends ago and also taking him off in Sunday's 1-1 draw with Rennes, Enrique admitted that PSG must become accustomed to playing without the World Cup winner as he closes in on his dream Blancos switch.
PSG managed to convince Mbappe to stay another two years in 2022, when he was originally expected to sign for Real Madrid on a free transfer, but he refused to take up the option to extend those terms until 2025 last summer.
Before severing ties with Les Parisiens, Mbappe is expected to meet with the Emir of Qatar alongside French president Emmanuel Macron on Tuesday, as the former undertakes an official two-day visit to the country.
It was rumoured that Sheikh Tamim could try to persuade Mbappe into performing another sensational U-turn on his future, but according to Fabrizio Romano, the Emir of Qatar will not be making a last-ditch attempt to keep the 25-year-old at PSG.
Sheikh Tamim is the founder of Qatar Sports Investments, the owners of PSG, but their meeting in midweek will not be related to Mbappe's future as the striker's move to Real Madrid is set in stone.
PSG president Nasser Al-Khelaifi has already been informed by Mbappe that he will not be remaining at the Parc des Princes no matter how much money is placed in front of him, and he will accept a significant pay cut to join Real Madrid.
Mbappe is understood to be pocketing a gargantuan €200m (£171.1m) per year at PSG, but Real refused to break their wage structure and only offered the ex-Monaco man €15m (£12.8m) each season.
However, Los Blancos have allegedly agreed to hand Mbappe a mammoth signing-on bonus of €128m (£109.5m), which will be paid to the attacker over the duration of his five-year contract.
A transfer to the Premier League with either Arsenal or Liverpool was briefly mooted, but neither side would have been expected to bow to Mbappe's economic demands, and the forward only had eyes on a move to Real.
Since first joining PSG on loan from Monaco in 2017, Mbappe has overtaken Edinson Cavani at the top of Les Parisiens' goalscoring charts with 244 strikes in 292 games, setting up 105 more.
The 25-year-old has won five Ligue 1 titles while representing the capital giants, although he is yet to fulfil his dream of becoming a Champions League winner with PSG, who overcame Real Sociedad 2-0 in the first leg of their last-16 tie earlier this month.