Salihamidzic told Sky (h/t Goal's Joe Wright) that he was not expecting his club to be busy in the transfer market.
"It's not good to speak about players from other clubs," he said ahead of the club's game against Wolfsburg on Saturday. "We will leave all options open for us in the transfer market, but I don't think much will happen."
Sane is currently sidelined after suffering an anterior cruciate ligament injury in August that saw Manchester City rule him out of action for seven months, per The Independent.
Bild (h/t the Mirror's Matt Maltby) have reported that Sane wants to move to the Allianz Arena in January and has made his intentions clear to Pep Guardiola's side.
The Manchester City boss has not ruled out an exit for Sane:
Sane joined Manchester City in 2016 from Schalke and has won two Premier League titles, the FA Cup and two League Cup crowns with the Citizens.
The winger was also named the PFA Young Player of the Year in 2018:
Sane has just 18 months left on his current Manchester City deal, and a move "looks inevitable" in either January or next summer, according to Goal's Jonathan Smith.
Bayern were interested in Sane in summer 2018 and prepared a bid of £73 million, although Manchester City valued the 23-year-old at £137 million, per James Ducker at the Telegraph.
Sane's value will have dropped as he has been out of action for so long, but Manchester City will not want to let such a talented players leave on the cheap.
Bild's Christian Falk has reported the German giants can afford to sign Sane in January:
Bayern Munich are four points behind RB Leipzig in the Bundesliga and could benefit from strengthening in the January transfer window.
The club saw veteran attackers Arjen Robben and Franck Ribery depart in the summer, while Kingsley Coman had been sidelined after suffering a knee injury against Tottenham Hotspur in the UEFA Champions League.