The 18-year-old, who has just a year left on his current contract has been a prime target for German champions Bayern Munich as Chelsea rejected four bids from the Bavarians for him in last January.
And Lampard insists the club will keep hold of their young players, stressing Hudson-Odoi could develop to become central to his plans at Chelsea.
“We want young players; you can see that. Other players are signing up around him and hopefully it [Hudson-Odoi’s new contract] is something that is going to be done.
“Of course, we want him to sign at this club and be a big player for us. I have spoken to him a couple of times because I want him to know how I feel.
“There are two things. One is the football side, which I am involved in, and one is the negotiating and making sure the contract is signed, which I am not.
“So to say I am confident would mean that I know every side, I don’t quite, I leave that to the club. What I do know is the club want Callum to sign.
“He is a player who has come through the Chelsea academy, broken into the England squad and he is, of course, potentially, a huge player now and in the future.
“Callum knows how I feel, he can be absolutely central to this team. He is young, there is a lot of improvement which is only good news for all of us. He is a really big talent.
“The fans love him here. The club want to love him.
“I have a real care for the players at this club, particularly the young players, and it is important I show that. Then the decision will be his and the club’s together.”
