The 18-year-old has been heavily linked with a January move to the Allianz Arena with Bayern reportedly making a number of bids to land the England youth international.
Chelsea boss Maurizio Sarri has urged Hudson-Odoi to remain with the Blues and handed him a start in Tuesday's 1-0 Carabao Cup semi-final first-leg defeat to Tottenham.
But Bayern, who trail league leaders Borussia Dortmund by six points, are still chasing their man and Salihamidzic sees Hudson-Odoi as an ideal player for the club.
"He is a very interesting player we really want to sign," he told German newspaper Bild during a winter training camp in Doha.
"He has qualities that fit our game. He can dribble, he is fast, he moves well towards the goal. He is a young player who has great potential to evolve.
"I see in him a really good player who would certainly be a good face to join us."
If Hudson-Odoi was to make the move to Germany he would become the latest English talent to head to the Bundesliga, with Jadon Sancho starring at Dortmund and Arsenal winger Reiss Nelson on loan at Hoffenheim.