Chelsea forward Hudson-Odoi has been impressed by Musiala after his England Under-21s debut.
Musiala, 17, was born in Germany but moved to England when he was seven and spent four months at Southampton before joining Chelsea and returning to Germany last year.
He has played for Germany's Under-16s but scored on his full England Under-21 bow, Tuesday's 5-0 win over Albania, and Hudson-Odoi admitted they have spoken about Musiala's international future.
"We talked about that. I said he should be staying with England. He knows a lot of the boys already and has been really welcomed into the team," said the 20-year-old, who also scored in the final Euro 2021 qualifier at Molineux.
"I said to him, 'I can't choose for you but it would be nice if you stayed with England'. Hopefully he gets to the seniors as quickly as possible.
"Jamal is a top, top player. I have known him from when he was at Chelsea. He is a great player and I've watched him for a while. He went to the same school as me as well.
"I wanted to welcome him to the Under-21s as soon as possible. He is a good guy, very shy, and before the game I wanted to see he was feeling himself and confident and not scared or shy.
"I said 'play your own game and get a goal for yourself' which he did. I was really happy for him. I have always said to him keep doing your thing day in day out and you will get to the seniors sooner rather than later.
"Wherever he is I will be watching him and see he is doing himself proud."
Musiala is just one of the Under-21s who can represent another country with Ebere Eze eligible for Nigeria and Jonathan Panzo and Marc Guehi able to play for the Ivory Coast.
Boss Aidy Boothroyd knows the Three Lions will eventually miss out on a player who has dual nationality and they are currently battling the USA for Valencia winger Yunus Musah.
The 17-year-old made his USA debut against Wales last week and now has two caps but Boothroyd has not given up on him.
He said: "We have known about it for a little while and I did speak to Yunus' father. I know a few coaches in the senior staff spoke to the family as well.
"We put our hat into the ring and we are keeping a close eye on things. I am hopeful we will see him in the Under-21s at some point. I don't know [if he has made his decision]. I hope he hasn't because I think if he came here and saw what we are all about that he would really enjoy it."