Bayern is planning a major squad overhaul this summer, and has already confirmed the signings of French World Cup winners Benjamin Pavard and Lucas Hernandez, AFP reported.
In an interview with German news agency dpa on Tuesday, Hoeness admitted that, in an ideal world, he would love to sign another French World Cup winner, Paris Saint-Germain's 20-year-old star.
"I would sign Mbappe straight away, he is a top player. But we don't have the money for him," said Hoeness.
The Bayern president ruled out spending €100 million on a single player in the summer transfer window, but suggested that Bayern may break that figure in the future.
"There definitely won't be a €100m transfer this year, but I have to admit that ten years ago, I couldn't have imagined spending 80 million," he said.
The sum of €80 million was what Bayern paid to sign Hernandez from Atletico Madrid, a figure nearly double that of the club’s previous record transfer – fellow Frenchman Corentin Tolisso.
In 22-year-old Kingsley Coman, Bayern has yet another Gallic talent in its emerging generation.
On Tuesday, club legend Lothar Matthaeus backed Coman and Serge Gnabry, 23, to follow in the footsteps of departing veterans Arjen Robben and Franck Ribery, who are both out of contract at the end of June.
"Coman and Gnabry are both quick, good dribblers and dangerous in front of goal," Matthaeus wrote in his column for Sky Sports, adding that "legendary" veterans Robben and Ribery would not be missed.