Bayern defensive mainstay Alaba has veteran agent Pini Zahavi on his side in talks over a new deal, with his present contract due to expire at the end of the 2020-2021 season.
However, Hoeness has indicated those discussions are not moving towards any resolution, and he says Alaba should make up his own mind about where he wants to spend the coming years.
Compared to Franz Beckenbauer by Karl-Heinz Rummenigge recently, Alaba has a hugely influential role at Bayern, who wrapped up a 2019-2020 treble by winning the Champions League in August.
Hoeness made Bayern's position regarding 28-year-old Alaba quite clear, saying it must be "very tough" to avoid disrupting its salary structure.
"We want him to stay because he is a great boy and player," Hoeness said. "I had a coffee with him a few weeks ago, but we haven't come to a conclusion yet.
"Hansi Flick really wants to keep him."
Hoeness said Zahavi is seeking a substantial fee for negotiating a deal, claiming he wanted something "in the double-digit million range" to secure Alaba's signature.
"That is not possible at all," Hoeness said.
The world's top agents can often earn huge sums, but Hoeness, who has stepped back from his previous role to become an honorary Bayern president, says Alaba should focus on what he wants from the rest of his career.
Austrian Alaba joined Bayern's academy in 2008 and has since gone on to win nine Bundesliga titles. He is reportedly admired by the likes of Manchester City and Barcelona.
"It's really all about money," Hoeness said. "He's already with the best club in the world, where else should he go? I think he shouldn't let himself be influenced from outside.
"I hope that David and his father understand that a four or five-year contract with Bayern is the best for them and they fit into our salary structure. Then everyone would be happy.
"The last millions that are involved don't make him happier, but they would mess up our salary structure. That's why the club has to be very tough on this."