He slapped in a transfer request two months ago in the wake of a £35million bid from Bayern Munich and a lack of first-team opportunities at Stamford Bridge.
But Southgate believes Hudson-Odoi, who made his England debut on Friday, can have a bright future with the Blues under Maurizio Sarri.
The Three Lions boss said: “If you look at number of appearances, he has actually been on the field quite a lot.
“And I know from when we were talking with the club earlier in the season how much faith Maurizio has in him. He has got some outstanding players just in front of him but he's slowly getting more and more game time.
“So, I think he's maturing well. There doesn't need to be a rush for him. We've seen that with Marcus Rashford and his development.
“He's getting first-team football and that's important. For us, I think his progress is good."