The Bundesliga side have made several bids for the 18-year-old winger, but Chelsea are stalling on their latest £35 million ($44.7m) offer as they hope to convince him to stay at Stamford Bridge.
Bayern have made no secret of their desire to bring in the England Under 19 international, with Salihamidzic revealing last week that they "really want to sign" him.
Blues boss Maurizio Sarri accused the Germans of a lack of professionalism over their public pursuit of Hudson-Odoi, while the English club will take the case to FIFA if there is any sign of "tapping up".
But Salihamidzic says the Bavarian side are not giving up on landing their top target just yet, despite Chelsea's attempts to discourage them.
"We want to sign the player," he told Sport Bild. "I am fully convinced of his abilities. We are in talks with Chelsea."
He added: "But we have many leaders in our team. That's why it would not be a problem if no player arrived in January. We have to find a good mix between young talents and experienced leaders who carry the team."
Bayern are yet to confirm if they will keep James Rodriguez on a permanent deal as his two-year loan from Real Madrid enters its final months.
It has been suggested that they could trigger the buying option in the summer and quickly sell him on for a profit, but Salihamidzic denied that is part of their plan.
"We'll look at the second half of the season and draw the right conclusions," he added. "That would not be Bayern's style. If we decide on a player then he remains part of Bayern."
The German champions have also been linked to a move for Atletico Madrid defender Lucas Hernandez, but have been told they will have to wait until the summer to land him.
"We have already had talks. There will be more. It is unrealistic for him to come in the winter," he said, before addressing the ongoing links to Ajax stars Frenkie de Jong and Matthijs de Ligt. "Both are very good players with great development potential. But we have to see what we have in store for the summer."