Luis Enrique's team would have sealed the title later on Wednesday if second-placed Monaco had failed to beat Lille at home, but the principality side prevailed 1-0 courtesy of Youssouf Fofana's second-half strike.
Mbappe, who is set to leave PSG in the summer with Real Madrid as the biggest favourite to sign him, told reporters that his future is not in his mind and that his focus is totally on bringing glory to the French capital.
Paris Saint-Germain overcame a controversial first-half sending-off to win 2-0 away to bitter rivals Marseille in Ligue 1 on Sunday, with Portuguese duo Vitinha and Goncalo Ramos scoring their goals.
The Euro 2024 favourites were left reeling after conceding just eight seconds into their game against Germany in Lyon last weekend, which they went on to lose 2-0.
"It is very difficult from a psychological and physical viewpoint to take part in two competitions like that one after the other, in the summer, without having any holiday," Deschamps admitted on Thursday.
"It's very simple, sooner or later, when it happens, we have to get used to playing without Kylian," Luis Enrique told the post-match press conference.
"Mbappe has communicated his decision to PSG but the terms of his exit are yet to be fully agreed. An official announcement is expected once the situation is finalised in the next few months," the report said.
"I was pleased with the whole match, I think my team is competitive each time and today was no exception," said PSG coach Luis Enrique.
Mbappe's contract with the Ligue 1 champions runs out at the end of June and he is free to sign an agreement to join a new club for next season.
Barcelona forked out fees in excess of 100 million euros ($109.24 million) for Philippe Coutinho, Antoine Griezmann and Ousmane Dembele between 2017-19, but the club's financial issues mean they are unlikely to splurge on big new signings anytime soon.
Arsenal's search for a proven goalscorer to spearhead their challenge for a first Premier League title since 2004 could also loom large.
"We are not a couple but that is mainly because he doesn't want us to be," the Spaniard joked.
The prestigious award has been dominated over the last 15 years by Messi and his old adversary Cristiano Ronaldo, who have won it 12 times between them.
PSG were eager to bounce back from their 4-1 defeat away to Newcastle United three weeks ago and they ultimately had too much attacking quality for their Italian visitors at the Parc des Princes.
"Throughout the match they were fresher than us," said Luis Enrique after his first loss as PSG coach.
Messi, who recently left Paris Saint-Germain for Inter Miami, is in with a chance of succeeding Karim Benzema and winning the Ballon d'Or for the eighth time in his remarkable career after leading Argentina to World Cup glory in Qatar last year
Ancelotti added that Real are unlikely to do any more transfer business in the current window which closes on Sept. 1.
Mbappe came off the bench to bury a spot-kick he earned just past the hour mark, but Toulouse equalised with a penalty of their own via Zakaria Aboukhlal four minutes from the end
A source close to PSG told AFP that 31-year-old Neymar "no longer figures in the club or manager's plans" with the Brazilian immediately linked to Al-Hilal in the Gulf kingdom