Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
The Germany midfielder, whose current deal expires next summer, has been heavily linked with a move to Manchester United, with reports claiming a deal between the two clubs is imminent.
New president Hopfner warned Bayern's current offer would not remain on the table indefinitely.
"There will certainly be further talks. But at some point the player has to say what he wants," Hopfner said in an interview with Kicker magazine.
"We will not exceed certain financial boundaries."
Hopfner pointed to the case of Michael Ballack, who left the club for Chelsea in 2006, as a similar example.
"It was the same with Michael Ballack and at some point we withdrew the offer."