The 20-year-old striker is this season's top scorer in Ligue 1 with 27 goals from 26 appearances, enhancing his reputation as one of the world's most promising young players.
A World Cup winner with France, Mbappe is seen as a successor to Cristiano Ronaldo and Lionel Messi as one of the best in the game.
Bayern chief Hoeness admits the Bundesliga champions would be happy to welcome the forward to Bavaria but he doubts any team can afford the fee PSG would demand for him.
"I would buy Mbappé immediately. The player is great. But we don't have the money necessary for that," Hoeness told Deutschen Presse-Agentur.
"It's not about whether Mbappe is worth the money. The question is: can anyone afford to spend this money without getting into financial trouble?
"I read that the most expensive picture in the world cost almost €400 million at an auction. Is a work of art worth it? Of course not! But if someone really wants to own it and pays so much for it, that's ultimately his decision."
While Europe's richest teams have driven transfer prices beyond the €100m mark, Bayern have been reluctant to spend big.
They recently spent a club record €80m (£68m/$90m) to sign Lucas Hernandez from Atletico Madrid this summer and Hoeness was surprised by the reaction to the deal.
“I was surprised that our €80 million was criticised so much. Recently, it was still being said that with a cautious transfer policy, Bayern have no chance of breaking into the group of English and Spanish top clubs and Paris Saint-Germain. Now we deliver and people shout: ‘How can you spend €80 million on a player?’ What would people have cried when we bought Kylian Mbappé?
He added: “We believe that the time has come for Bayern to put their hard-earned money on the market to bring back a new, young team to the pitch.”