German giants Bayern Munich have tabled numerous bids, of up to £35million.
Lampard, now in his first season of management with Championship promotion contenders Derby, said: “I would like to think a young English player at 18, who has his nose in the first team and has incredible talent, will stay and will push himself into the team and be a big player for Chelsea and England.
“Being close to Chelsea, I want him to stay there. It is a great club, a fantastic club.
“He needs to stay there and work hard to get chances to play in the team. He has done that recently and he has played, and done very well in the last couple of games. Hopefully we will see more of that. I think it is a great opportunity for him to do that.
“But in terms of what Chelsea think, what Callum thinks and what the interest is from other clubs, that is for them to sort out."