The 23-year-old has been linked with a departure from City after playing a reduced role in their treble-winning campaign, starting 30 of his 47 appearances in all competitions.
German champions Bayern have emerged as the top candidates to sign Sane after seeing star attackers Arjen Robben and Franck Ribery leave.
Bayern sporting director Hasan Salihamidzic was asked about reports suggesting the Bavarian outfit are chasing the former Schalke player and did not dismiss the possibility.
"I don't comment on names," he said when quizzed on Sane, but added that a few more signings are expected this summer as Hoeness has given a €200 million transfer budget, according to Sport Bild .
"We will try to do something for the new season, so we must also clarify how much money we have available for it," he added.
But Hoeness has since clarified that the Bundesliga champions are already advancing on their interest.
"We are dealing with this player," Hoeness told Sueddeutsche Zeitung .
Bayern striker Robert Lewandowski encouraged the club to go after Sane as he believes the Germany international would improve the squad.
"I’ve already seen many times how good he is," he said . "That’s a player who can immediately take us higher, who improves the team."
But City are not ready to let the winger leave just yet, as coach Pep Guardiola believes he is still a crucial part of the team.
"We are one-and-a-half years trying to sign his [new] contract. We want him," he told reporters recently .
"If you want to extend his contract, it's because you want him. You're not going to extend his contract because you don't want him."
He added: "He's competing with Raheem Sterling and Bernardo Silva. It's not easy. If you want to play in for competitions for the quadruple we need Leroy, Sterling, Riyad Mahrez, Bernardo, we can't compete for the quadruple with just two wingers."
Sane's compatriot and City team-mate Ilkay Gundogan reiterated Guardiola's message dismissing speculation over a transfer.
"If players in our team at one or another time do not play, it has now become a normal fact that there are automatic rumours," he told Sport Bild last week .
"As our coach has already said, the club wants to keep Leroy."