Bundesliga giants Bayern were again interested in the England star though a move never materialised.
Hudson-Odoi has not let it get to his head having come off the bench to score as Chelsea fought back from 3-0 down to earn a draw against West Brom.
He then started the last Premier League game against Crystal Palace and could feature this weekend against Southampton.
Bayern may remain keen having been knocked back by Chelsea this summer with Salihamidzic hinting that demands were too high.
“There are transfers that come to the point where you have to say: ‘We have to leave this immediately’,” Salihamidzic told Sport Bild.
“It is all the more important that one thinks about alternatives or alternative paths right from the start.
“We negotiated with Chelsea but there was no agreement. That happens.”
Bayern boss Hansi Flick recently hailed Hudson-Odoi’s talent and versatility, hinting that a move could still happen in the future.
“He is one of the greatest talents in that position,” Flick said of the Chelsea winger.
“He can play wide and as a No. 10 so it’s entirely legitimate that we at Bayern Munich are interested in him.”
Chelsea boss Frank Lampard wants to keep his man, saying after the win over Palace: “Callum is absolutely part of my plans here. We have [Christian] Pulisic and Hakim Ziyech injured before Christian came back in today.
Get the latest transfer news straight into your inbox!
Want to be on the ball with all of the latest football news?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
“We need options and what Callum showed today and the second half against West Brom is exactly what he needs to show. I am pleased with him.
“At the minute we know we’re missing Christian Pulisic and Hakim Ziyech, who are probably the most natural wingers in our team along with Callum.
“What I did like is that Callum fronts up his left back and tries to go by him. That was missing with Cal during the first half, he was playing too safe coming inside.”