The attacker was nearly signed by Bayern Munich in recent days, but a loan with an option to buy agreement fell through.
Now Hudson-Odoi must fight for his place with the Blues, and Lampard has spoken about where he wants the Englishman to improve.
"I am not sure I want to compare him [Hudson-Odoi] to Willian, they both have some aspects but they are not as similar as you might think," Lampard told reporters, via Goal.
"With Callum, his work off the ball is something I am trying to improve because at this level in the Premier League, you see how we worked last year, and Willian was the first trigger in us winning the ball back.
"He covered so much ground in high areas, at speed, off the ball. Wingers have to have that mindset these days. That's something I put on Callum and he has to improve on little bits and he did better, but he can still do more.
"I think Callum's natural ability is on the ball, taking people on the outside and that's what he can do, and those things will come out as Callum keeps developing. As he builds confidence, he needs to know that I am behind him in that sense because he can bring a lot. Then, we will see a lot more from Callum.
"We have to remember he had a very difficult injury to overcome at a very young age. It is not easy to do that when you are a player with pace, trickery and explosiveness of that nature.
"I think this season Callum can offer a lot for us in those terms because of his natural ability."