As revealed by Goal , Hudson-Odoi, who has started the Blues' last two games, is a top January target for the Bundesliga side, with a fourth bid of £35m ($45m) having been made on Tuesday .
Bayern have also offered the 18-year-old the No.10 shirt at the club - a squad number that will be available when Arjen Robben moves on in the summer.
And Salihamidzic has confirmed that the club are keen on signing the winger, telling reporters at Bayern's winter training camp in Doha: "He's a very interesting player that we really want to sign.
"He has qualities that suit our game. He's a strong dribbler, fast, and carries a goal threat."
Bayern are on the look-out for wingers with Robben confirming he will leave at the end of the season and Salihamidzic admitting on Wednesday "it's probably going to be Franck [Ribery's] last year".
Hudson-Odoi would certainly fill one of those voids and, if he does move, would continue the trend of young English players thriving in the Bundesliga.
Sometimes you win, sometimes you learn...! pic.twitter.com/2UvjiOs6xQ— Callum Hudson-Odoi (@Calteck10) January 8, 2019
Speaking after Tuesday's first-leg defeat to Tottenham in the Carabao Cup semi-finals, Chelsea boss Maurizio Sarri insisted Hudson-Odoi had not been distracted by the speculation.
The Italian said: "Odoi in the last week has been very normal. I have seen him every day in training, he has been really very normal.
"He is improving, in the last match he played very well and also today I think a very good match.
"He played like a player of 25 or 26 years, I think – very good match of application, very good in the defensive phase, very, very good.
"He was completely normal in this period. I don't know, maybe he doesn't read anything."