Hudson-Odoi, who was the subject of a failed bid of £35m from German champions Bayern Munich in the January transfer window, played 23 times in all competitions for Chelsea last season and scored five goals.
Hudson-Odoi submitted a transfer request when Bayern Munich tabled their offer, after becoming frustrated over a lack of first-team opportunities whiles his peers, like Jadon Sancho of Borussia Dortmund, were sparkling for their sides.
The 18-year-old saw his season curtailed by an Achilles injury suffered against Burnley in the Premier League in April and is scheduled to resume full training before the start of the 2019/2020 season.
Bayern Munich are hoping to resurrect a deal for Hudson-Odoi, whose Chelsea contract runs out at the end of the 2019/2020 season, after the departures of Arjen Robben and Franck Ribery.
Lampard was appointed as Maurizio Sarri’s successor last week on a three-year deal and the former Derby County manager believes Hudson-Odoi can fulfill his potential if he stays at Stamford Bridge.
"I have seen Callum come through and he is a fantastic talent," Lampard said.
"We all know that and I will speak to him and I want him to stay.
"I know the club want him to stay and he is going to be central for us on the pitch. That is the opportunity that is really in front of him now, certainly from where I am sitting.
"There are things as a young player that he will want to improve and there are things through natural development that will improve, so I am not going to say things that are pie in the sky but with his talent he can be central to this team, he can be central to England.
"I want to work with him, I want to drive him forward and I want to improve him as a player.
"He can show, right here at Chelsea, at the club where he came through the academy, that he is going to be a world-class player, because I truly believe that."
